diff --git a/UPDATE_LEAN.sh b/UPDATE_LEAN.sh
index 3ea0fe4..34f979f 100644
--- a/UPDATE_LEAN.sh
+++ b/UPDATE_LEAN.sh
@@ -5,11 +5,15 @@ cd $(dirname $0)
 
 cd server
 
-cd testgame
+cd adam
 lake update
 
 cp lake-packages/mathlib/lean-toolchain lean-toolchain
 cp lake-packages/mathlib/lean-toolchain ../leanserver/lean-toolchain
+cp lake-packages/mathlib/lean-toolchain ../nng/lean-toolchain
 
 cd ../leanserver
 lake update
+
+cd ../nng
+lake update
diff --git a/client/src/App.tsx b/client/src/App.tsx
index c1eb545..3c06cb9 100644
--- a/client/src/App.tsx
+++ b/client/src/App.tsx
@@ -1,6 +1,6 @@
 import * as React from 'react';
 import { useState, useEffect } from 'react';
-import { Outlet } from "react-router-dom";
+import { Outlet, useParams } from "react-router-dom";
 
 import '@fontsource/roboto/300.css';
 import '@fontsource/roboto/400.css';
@@ -10,10 +10,15 @@ import '@fontsource/roboto/700.css';
 import './reset.css';
 import './app.css';
 
+export const GameIdContext = React.createContext<string>(undefined);
+
 function App() {
+  const params = useParams();
   return (
     <div className="app">
-      <Outlet />
+      <GameIdContext.Provider value={params.gameId}>
+        <Outlet />
+      </GameIdContext.Provider>
     </div>
   )
 }
diff --git a/client/src/components/Inventory.tsx b/client/src/components/Inventory.tsx
index bde6c8e..2135760 100644
--- a/client/src/components/Inventory.tsx
+++ b/client/src/components/Inventory.tsx
@@ -5,6 +5,7 @@ import { FontAwesomeIcon } from '@fortawesome/react-fontawesome'
 import { faLock, faLockOpen, faBook, faHammer, faBan } from '@fortawesome/free-solid-svg-icons'
 import Markdown from './Markdown';
 import { useLoadDocQuery, ComputedInventoryItem } from '../state/api';
+import { GameIdContext } from '../App';
 
 export function Inventory({ tactics, lemmas, definitions, setInventoryDoc } :
   {lemmas: ComputedInventoryItem[],
@@ -55,14 +56,14 @@ function InventoryList({items, docType, openDoc} : {items: ComputedInventoryItem
     ).map(item => {
         if (tab == item.category) {
           return <InventoryItem key={item.name} showDoc={() => {openDoc(item.name, docType)}}
-            name={item.name} locked={item.locked} disabled={item.disabled} />
+            name={item.name} displayName={item.displayName} locked={item.locked} disabled={item.disabled} />
         }
       }) }
     </div>
     </>
 }
 
-function InventoryItem({name, locked, disabled, showDoc}) {
+function InventoryItem({name, displayName, locked, disabled, showDoc}) {
   const icon = locked ? <FontAwesomeIcon icon={faLock} /> :
                disabled ? <FontAwesomeIcon icon={faBan} /> : ""
   const className = locked ? "locked" : disabled ? "disabled" : ""
@@ -73,15 +74,15 @@ function InventoryItem({name, locked, disabled, showDoc}) {
     }
   }
 
-  return <div className={`item ${className}`} onClick={handleClick}>{icon} {name}</div>
+  return <div className={`item ${className}`} onClick={handleClick}>{icon} {displayName}</div>
 }
 
 export function Documentation({name, type}) {
-
-  const doc = useLoadDocQuery({type: type, name: name})
+  const gameId = React.useContext(GameIdContext)
+  const doc = useLoadDocQuery({game: gameId, type: type, name: name})
 
   return <>
-    <h2 className="doc">{doc.data?.name}</h2>
+    <h2 className="doc">{doc.data?.displayName}</h2>
     <Markdown>{doc.data?.text}</Markdown>
   </>
 }
diff --git a/client/src/components/Level.tsx b/client/src/components/Level.tsx
index 7f4437b..513a8ed 100644
--- a/client/src/components/Level.tsx
+++ b/client/src/components/Level.tsx
@@ -22,7 +22,7 @@ import './level.css'
 import { Button } from './Button'
 import { ConnectionContext, useLeanClient } from '../connection';
 import { useGetGameInfoQuery, useLoadLevelQuery } from '../state/api';
-import { codeEdited, selectCode, progressSlice, selectCompleted } from '../state/progress';
+import { changedSelection, codeEdited, selectCode, selectSelections, progressSlice, selectCompleted } from '../state/progress';
 import { useAppDispatch, useAppSelector } from '../hooks';
 import { useStore } from 'react-redux';
 
@@ -40,6 +40,7 @@ import Markdown from './Markdown';
 
 import Split from 'react-split'
 import { Alert } from '@mui/material';
+import { GameIdContext } from '../App';
 
 export const MonacoEditorContext = React.createContext<monaco.editor.IStandaloneCodeEditor>(null as any);
 
@@ -75,7 +76,9 @@ function PlayableLevel({worldId, levelId}) {
   const codeviewRef = useRef<HTMLDivElement>(null)
   const introductionPanelRef = useRef<HTMLDivElement>(null)
 
-  const initialCode = useAppSelector(selectCode(worldId, levelId))
+  const gameId = React.useContext(GameIdContext)
+  const initialCode = useAppSelector(selectCode(gameId, worldId, levelId))
+  const initialSelections = useAppSelector(selectSelections(gameId, worldId, levelId))
 
   const [commandLineMode, setCommandLineMode] = useState(true)
   const [commandLineInput, setCommandLineInput] = useState("")
@@ -86,6 +89,8 @@ function PlayableLevel({worldId, levelId}) {
   useEffect(() => {
     // Scroll to top when loading a new level
     introductionPanelRef.current!.scrollTo(0,0)
+    // Reset command line input when loading a new level
+    setCommandLineInput("")
   }, [levelId])
 
   React.useEffect(() => {
@@ -122,24 +127,48 @@ function PlayableLevel({worldId, levelId}) {
     }]);
   }
 
-  const connection = React.useContext(ConnectionContext)
-
-  const gameInfo = useGetGameInfoQuery()
-
-  const level = useLoadLevelQuery({world: worldId, level: levelId})
+  const gameInfo = useGetGameInfoQuery({game: gameId})
+  const level = useLoadLevelQuery({game: gameId, world: worldId, level: levelId})
 
   const dispatch = useAppDispatch()
 
   const onDidChangeContent = (code) => {
-    dispatch(codeEdited({world: worldId, level: levelId, code}))
+    dispatch(codeEdited({game: gameId, world: worldId, level: levelId, code}))
 
     setCanUndo(code.trim() !== "")
   }
 
-  const completed = useAppSelector(selectCompleted(worldId, levelId))
+  const onDidChangeSelection = (monacoSelections) => {
+    const selections = monacoSelections.map(
+      ({selectionStartLineNumber, selectionStartColumn, positionLineNumber, positionColumn}) =>
+      {return {selectionStartLineNumber, selectionStartColumn, positionLineNumber, positionColumn}})
+    dispatch(changedSelection({game: gameId, world: worldId, level: levelId, selections}))
+  }
+
+  const completed = useAppSelector(selectCompleted(gameId, worldId, levelId))
 
   const {editor, infoProvider, editorConnection} =
-  useLevelEditor(worldId, levelId, codeviewRef, initialCode, onDidChangeContent)
+    useLevelEditor(worldId, levelId, codeviewRef, initialCode, initialSelections, onDidChangeContent, onDidChangeSelection)
+
+  // Effect when command line mode gets enabled
+  useEffect(() => {
+    if (editor && commandLineMode) {
+      let endPos = editor.getModel().getFullModelRange().getEndPosition()
+      if (editor.getModel().getLineContent(endPos.lineNumber).trim() !== "") {
+        editor.executeEdits("command-line", [{
+          range: monaco.Selection.fromPositions(endPos, endPos),
+          text: "\n",
+          forceMoveMarkers: true
+        }]);
+      }
+      endPos = editor.getModel().getFullModelRange().getEndPosition()
+      let currPos = editor.getPosition()
+      if (currPos.column != 1 || (currPos.lineNumber != endPos.lineNumber && currPos.lineNumber != endPos.lineNumber - 1)) {
+        // This is not a position that would naturally occur from CommandLine, reset:
+        editor.setSelection(monaco.Selection.fromPositions(endPos, endPos))
+      }
+    }
+  }, [editor, commandLineMode])
 
   const [inventoryDoc, setInventoryDoc] = useState<{name: string, type: string}>(null)
 
@@ -151,9 +180,9 @@ function PlayableLevel({worldId, levelId}) {
     <Split minSize={0} snapOffset={200} sizes={[50, 25, 25]} className={`app-content level ${level.isLoading ? 'hidden' : ''}`}>
       <div className="exercise-panel">
         <div ref={introductionPanelRef} className="introduction-panel">
-          <Alert severity="info" sx={{ mt: 1 }}>
+          <div className="message info">
             <Markdown>{level?.data?.introduction}</Markdown>
-          </Alert>
+          </div>
         </div>
         <div className="exercise">
           {/* <h4>Aufgabe:</h4> */}
@@ -177,10 +206,12 @@ function PlayableLevel({worldId, levelId}) {
         </EditorContext.Provider>
 
         {completed && <div className="conclusion">
-          <Markdown>{level?.data?.conclusion}</Markdown>
+          <div className="message info">
+            <Markdown>{level?.data?.conclusion}</Markdown>
+          </div>
           {levelId >= gameInfo.data?.worldSize[worldId] ?
-          <Button to={`/`}><FontAwesomeIcon icon={faHome} /></Button> :
-          <Button to={`/world/${worldId}/level/${levelId + 1}`}>
+          <Button to={`/game/${gameId}`}><FontAwesomeIcon icon={faHome} /></Button> :
+          <Button to={`/game/${gameId}/world/${worldId}/level/${levelId + 1}`}>
             Next&nbsp;<FontAwesomeIcon icon={faArrowRight} /></Button>}
 
         </div>}
@@ -200,23 +231,24 @@ function PlayableLevel({worldId, levelId}) {
 export default Level
 
 function Introduction({worldId}) {
-  const gameInfo = useGetGameInfoQuery()
+  const gameId = React.useContext(GameIdContext)
+  const gameInfo = useGetGameInfoQuery({game: gameId})
 
   return <>
     <div style={gameInfo.isLoading ? null : {display: "none"}} className="app-content loading"><CircularProgress /></div>
     <LevelAppBar isLoading={gameInfo.isLoading} levelTitle="Einführung" worldId={worldId} levelId={0} />
     <div style={gameInfo.isLoading ? {display: "none"} : null} className="exercise-panel">
       <div className="introduction-panel">
-        <Alert severity="info" sx={{ mt: 1 }}>
+        <div className="message info">
           <Markdown>
             {gameInfo.data?.worlds.nodes[worldId].introduction}
           </Markdown>
-        </Alert>
+        </div>
       </div>
       <div className="conclusion">
         {0 == gameInfo.data?.worldSize[worldId] ?
-        <Button to={`/`}><FontAwesomeIcon icon={faHome} /></Button> :
-        <Button to={`/world/${worldId}/level/1`}>
+        <Button to={`/game/${gameId}`}><FontAwesomeIcon icon={faHome} /></Button> :
+        <Button to={`/game/${gameId}/world/${worldId}/level/1`}>
           Start&nbsp;<FontAwesomeIcon icon={faArrowRight} />
         </Button>}
       </div>
@@ -225,11 +257,12 @@ function Introduction({worldId}) {
 }
 
 function LevelAppBar({isLoading, levelId, worldId, levelTitle}) {
-  const gameInfo = useGetGameInfoQuery()
+  const gameId = React.useContext(GameIdContext)
+  const gameInfo = useGetGameInfoQuery({game: gameId})
 
   return <div className="app-bar" style={isLoading ? {display: "none"} : null} >
     <div>
-    <Button to={`/`}><FontAwesomeIcon icon={faHome} /></Button>
+    <Button to={`/game/${gameId}`}><FontAwesomeIcon icon={faHome} /></Button>
       <span className="app-bar-title">
         {gameInfo.data?.worlds.nodes[worldId].title && `World: ${gameInfo.data?.worlds.nodes[worldId].title}`}
       </span>
@@ -239,19 +272,20 @@ function LevelAppBar({isLoading, levelId, worldId, levelTitle}) {
         {levelTitle}
       </span>
       <Button disabled={levelId <= 0} inverted={true}
-        to={`/world/${worldId}/level/${levelId - 1}`}
+        to={`/game/${gameId}/world/${worldId}/level/${levelId - 1}`}
         ><FontAwesomeIcon icon={faArrowLeft} />&nbsp;Previous</Button>
       <Button disabled={levelId >= gameInfo.data?.worldSize[worldId]} inverted={true}
-        to={`/world/${worldId}/level/${levelId + 1}`}
+        to={`/game/${gameId}/world/${worldId}/level/${levelId + 1}`}
         >Next&nbsp;<FontAwesomeIcon icon={faArrowRight} /></Button>
     </div>
 
   </div>
 }
 
-function useLevelEditor(worldId: string, levelId: number, codeviewRef, initialCode, onDidChangeContent) {
+function useLevelEditor(worldId: string, levelId: number, codeviewRef, initialCode, initialSelections, onDidChangeContent, onDidChangeSelection) {
 
   const connection = React.useContext(ConnectionContext)
+  const gameId = React.useContext(GameIdContext)
 
   const [editor, setEditor] = useState<monaco.editor.IStandaloneCodeEditor|null>(null)
   const [infoProvider, setInfoProvider] = useState<null|InfoProvider>(null)
@@ -278,7 +312,7 @@ function useLevelEditor(worldId: string, levelId: number, codeviewRef, initialCo
       theme: 'vs-code-theme-converted'
     })
 
-    const infoProvider = new InfoProvider(connection.getLeanClient())
+    const infoProvider = new InfoProvider(connection.getLeanClient(gameId))
 
     const editorApi = infoProvider.getApi()
 
@@ -328,7 +362,7 @@ function useLevelEditor(worldId: string, levelId: number, codeviewRef, initialCo
     return () => { infoProvider.dispose(); editor.dispose() }
   }, [])
 
-  const {leanClient, leanClientStarted} = useLeanClient()
+  const {leanClient, leanClientStarted} = useLeanClient(gameId)
 
   // Create model when level changes
   useEffect(() => {
@@ -340,8 +374,11 @@ function useLevelEditor(worldId: string, levelId: number, codeviewRef, initialCo
         model = monaco.editor.createModel(initialCode, 'lean4', uri)
       }
       model.onDidChangeContent(() => onDidChangeContent(model.getValue()))
+      editor.onDidChangeCursorSelection(() => onDidChangeSelection(editor.getSelections()))
       editor.setModel(model)
-      editor.setPosition(model.getFullModelRange().getEndPosition())
+      if (initialSelections) {
+        editor.setSelections(initialSelections)
+      }
 
       infoviewApi.serverRestarted(leanClient.initializeResult)
       infoProvider.openPreview(editor, infoviewApi)
@@ -358,7 +395,8 @@ function useLevelEditor(worldId: string, levelId: number, codeviewRef, initialCo
 
 /** Open all files in this world on the server so that they will load faster when accessed */
 function useLoadWorldFiles(worldId) {
-  const gameInfo = useGetGameInfoQuery()
+  const gameId = React.useContext(GameIdContext)
+  const gameInfo = useGetGameInfoQuery({game: gameId})
   const store = useStore()
 
   useEffect(() => {
@@ -370,7 +408,7 @@ function useLoadWorldFiles(worldId) {
         if (model) {
           models.push(model)
         } else {
-          const code = selectCode(worldId, levelId)(store.getState())
+          const code = selectCode(gameId, worldId, levelId)(store.getState())
           models.push(monaco.editor.createModel(code, 'lean4', uri))
         }
       }
diff --git a/client/src/components/PrivacyPolicy.tsx b/client/src/components/PrivacyPolicy.tsx
new file mode 100644
index 0000000..774cc36
--- /dev/null
+++ b/client/src/components/PrivacyPolicy.tsx
@@ -0,0 +1,52 @@
+import { faShield } from '@fortawesome/free-solid-svg-icons';
+import { FontAwesomeIcon } from '@fortawesome/react-fontawesome';
+import * as React from 'react'
+
+const PrivacyPolicy: React.FC = () => {
+  const [open, setOpen] = React.useState(false);
+  const handleOpen = () => setOpen(true);
+  const handleClose = () => setOpen(false);
+
+  return (
+    <span>
+          <div className="privacy" onClick={handleOpen} title="Privacy Policy &amp; Impressum">
+            <FontAwesomeIcon icon={faShield} />
+            <p className="p1">legal</p>
+            <p className="p2">notes</p>
+          </div>
+      {open?
+        <div className="modal-wrapper">
+          <div className="modal-backdrop" onClick={handleClose} />
+          <div className="modal">
+            <div className="codicon codicon-close modal-close" onClick={handleClose}></div>
+            <h2>Privacy Policy &amp; Impressum</h2>
+
+            <p>Our server collects metadata (such as IP address, browser, operating system)
+            and the data that the user enters into the editor. The data is used to
+            compute the Lean output and display it to the user. The information will be stored
+            as long as the user stays on our website and will be deleted immediately afterwards.
+            We keep logs to improve our software, but the contained data is anonymized.</p>
+
+            <p>We do not use cookies, but your game progress is stored in the browser
+              as site data. Your game progress is not saved on the server; if you delete
+              your browser storage, it is completely gone.
+            </p>
+
+            <p>Our server is located in Germany.</p>
+
+            <p><strong>Contact information:</strong><br />
+              Jon Eugster<br />
+              Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf<br />
+              Universitätsstr. 1<br />
+              40225 Düsseldorf<br />
+              Germany<br />
+              <a href="mailto:jon.eugster@hhu.de">jon.eugster@hhu.de</a>
+
+            </p>
+          </div>
+        </div> : null}
+    </span>
+  )
+}
+
+export default PrivacyPolicy
diff --git a/client/src/components/Welcome.tsx b/client/src/components/Welcome.tsx
index 1c97932..a69d37f 100644
--- a/client/src/components/Welcome.tsx
+++ b/client/src/components/Welcome.tsx
@@ -5,7 +5,9 @@ import cytoscape, { LayoutOptions } from 'cytoscape'
 import klay from 'cytoscape-klay';
 import { useNavigate } from 'react-router-dom';
 import { useSelector } from 'react-redux';
+import Split from 'react-split'
 
+import PrivacyPolicy from './PrivacyPolicy';
 
 cytoscape.use( klay );
 
@@ -14,14 +16,25 @@ import { useGetGameInfoQuery } from '../state/api';
 import { Link } from 'react-router-dom';
 import Markdown from './Markdown';
 import { selectCompleted } from '../state/progress';
+import { GameIdContext } from '../App';
 
+const N = 24          // max number of levels per world
+const R = 800         // radius of a world
+const r = 110          // radius of a level
+const s = 100         // global scale
+const padding = 2000  // padding of the graphic (on a different scale)
 
 function LevelIcon({ worldId, levelId, position }) {
-  const completed = useSelector(selectCompleted(worldId,levelId))
+  const gameId = React.useContext(GameIdContext)
+  const completed = useSelector(selectCompleted(gameId, worldId,levelId))
+
+  const x = s * position.x + Math.sin(levelId * 2 * Math.PI / N) * (R + 1.2*r + 2*Math.floor((levelId - 1)/N))
+  const y = s * position.y - Math.cos(levelId * 2 * Math.PI / N) * (R + 1.2*r + 2*Math.floor((levelId - 1)/N))
+
   // TODO: relative positioning?
   return (
-    <Link to={`/world/${worldId}/level/${levelId}`} key={`/world/${worldId}/level/${levelId}`}>
-      <circle fill={completed ? "green" :"#aaa"} cx={position.x + Math.sin(levelId/5) * 9} cy={position.y - Math.cos(levelId/5) * 9} r="0.8" />
+    <Link to={`/game/${gameId}/world/${worldId}/level/${levelId}`} key={`/game/${gameId}/world/${worldId}/level/${levelId}`}>
+      <circle fill={completed ? "green" :"#999"} cx={x} cy={y} r={r} />
     </Link>
   )
 }
@@ -29,7 +42,8 @@ function LevelIcon({ worldId, levelId, position }) {
 function Welcome() {
   const navigate = useNavigate();
 
-  const gameInfo = useGetGameInfoQuery()
+  const gameId = React.useContext(GameIdContext)
+  const gameInfo = useGetGameInfoQuery({game: gameId})
 
   const { nodes, bounds }: any = gameInfo.data ? computeWorldLayout(gameInfo.data?.worlds) : {nodes: []}
 
@@ -39,56 +53,66 @@ function Welcome() {
     }
   }, [gameInfo.data?.title])
 
-  const padding = 20
-
   const svgElements = []
 
   if (gameInfo.data) {
     for (let i in gameInfo.data.worlds.edges) {
       const edge = gameInfo.data.worlds.edges[i]
       svgElements.push(
-        <line key={`pathway${i}`} x1={nodes[edge[0]].position.x} y1={nodes[edge[0]].position.y}
-          x2={nodes[edge[1]].position.x} y2={nodes[edge[1]].position.y} stroke="#1976d2" strokeWidth="1"/>
+        <line key={`pathway${i}`} x1={s*nodes[edge[0]].position.x} y1={s*nodes[edge[0]].position.y}
+          x2={s*nodes[edge[1]].position.x} y2={s*nodes[edge[1]].position.y} stroke="#1976d2" strokeWidth={s}/>
       )
     }
+
     for (let id in nodes) {
       let position: cytoscape.Position = nodes[id].position
 
-      svgElements.push(
-        <Link key={`world${id}`} to={`/world/${id}/level/0`}>
-          <circle className="world-circle" cx={position.x} cy={position.y} r="8" />
-          <text className="world-name"
-            x={position.x} y={position.y}>{nodes[id].data.title ? nodes[id].data.title : id}</text>
-        </Link>
-      )
-
       for (let i = 1; i <= gameInfo.data.worldSize[id]; i++) {
         svgElements.push(
           <LevelIcon position={position} worldId={id} levelId={i} />
         )
       }
+
+      svgElements.push(
+        <Link key={`world${id}`} to={`/game/${gameId}/world/${id}/level/0`}>
+          <circle className="world-circle" cx={s*position.x} cy={s*position.y} r={R}
+              fill="#1976d2"/>
+          <foreignObject className="world-title-wrapper" x={s*position.x} y={s*position.y}
+              width={1.42*R} height={1.42*R} transform={"translate("+ -.71*R +","+ -.71*R +")"}>
+            <div>
+              <p className="world-title" style={{fontSize: Math.floor(R/4) + "px"}}>
+                {nodes[id].data.title ? nodes[id].data.title : id}
+              </p>
+            </div>
+          </foreignObject>
+        </Link>
+      )
     }
   }
 
-  return <div>
+  return <div className="app-content ">
   { gameInfo.isLoading?
-    <Box display="flex" alignItems="center" justifyContent="center" sx={{ height: "calc(100vh - 64px)" }}><CircularProgress /></Box>
+    <Box display="flex" alignItems="center" justifyContent="center" sx={{ height: "calc(100vh - 64px)" }}>
+      <CircularProgress />
+    </Box>
     :
-    <div className="app-content">
-      <Box sx={{ m: 3 }}>
-        <Typography variant="body1" component="div">
+    <Split className="welcome" minSize={200} sizes={[70, 30]}>
+      <div className="column">
+        <Typography variant="body1" component="div" className="welcome-text">
           <Markdown>{gameInfo.data?.introduction}</Markdown>
         </Typography>
-      </Box>
-      <Box textAlign='center' sx={{ m: 5 }}>
-        <svg xmlns="http://www.w3.org/2000/svg" xmlnsXlink="http://www.w3.org/1999/xlink" width="30%"
-            viewBox={bounds ? `${bounds.x1 - padding} ${bounds.y1 - padding} ${bounds.x2 - bounds.x1 + 2 * padding} ${bounds.y2 - bounds.y1 + 2 * padding}` : ''}>
-          {svgElements}
-        </svg>
-      </Box>
-    </div>
+      </div>
+      <div className="column">
+        <Box textAlign='center' sx={{ m: 5 }}>
+          <svg xmlns="http://www.w3.org/2000/svg" xmlnsXlink="http://www.w3.org/1999/xlink"
+              viewBox={bounds ? `${s*bounds.x1 - padding} ${s*bounds.y1 - padding} ${s*bounds.x2 - s*bounds.x1 + 2 * padding} ${s*bounds.y2 - s*bounds.y1 + 2 * padding}` : ''}>
+            {svgElements}
+          </svg>
+        </Box>
+      </div>
+    </Split>
   }
-
+    <PrivacyPolicy/>
   </div>
 }
 
@@ -116,9 +140,8 @@ function computeWorldLayout(worlds) {
     headless: true,
     styleEnabled: false
   })
-// TODO: Jon play around with graph layout
 
-  const layout = cy.layout({name: "klay", klay: {direction: "DOWN"}} as LayoutOptions).run()
+  const layout = cy.layout({name: "klay", klay: {direction: "DOWN", nodePlacement: "LINEAR_SEGMENTS"}} as LayoutOptions).run()
   let nodes = {}
   cy.nodes().forEach((node, id) => {
     nodes[node.id()] = {
diff --git a/client/src/components/infoview/CommandLine.tsx b/client/src/components/infoview/CommandLine.tsx
index b565761..72fa488 100644
--- a/client/src/components/infoview/CommandLine.tsx
+++ b/client/src/components/infoview/CommandLine.tsx
@@ -170,21 +170,6 @@ export function CommandLine() {
     return () => { l.dispose() }
   }, [oneLineEditor, runCommand])
 
-  // Effect when command line mode gets enabled
-  useEffect(() => {
-    if (commandLineMode) {
-      const endPos = editor.getModel().getFullModelRange().getEndPosition()
-      if (editor.getModel().getLineContent(endPos.lineNumber).trim() !== "") {
-        editor.executeEdits("command-line", [{
-          range: monaco.Selection.fromPositions(endPos, endPos),
-          text: commandLineInput + "\n",
-          forceMoveMarkers: false
-        }]);
-      }
-      editor.setPosition(editor.getModel().getFullModelRange().getEndPosition())
-    }
-  }, [commandLineMode])
-
   const handleSubmit : React.FormEventHandler<HTMLFormElement> = (ev) => {
     ev.preventDefault()
     runCommand()
diff --git a/client/src/components/infoview/hints.tsx b/client/src/components/infoview/hints.tsx
index 4a290fc..b7ba2b9 100644
--- a/client/src/components/infoview/hints.tsx
+++ b/client/src/components/infoview/hints.tsx
@@ -4,7 +4,7 @@ import { Alert, FormControlLabel, Switch } from '@mui/material';
 import Markdown from '../Markdown';
 
 function Hint({hint} : {hint: GameHint}) {
-  return <Alert severity="info" sx={{ mt: 1 }}><Markdown>{hint.text}</Markdown></Alert>
+  return <div className="message info"><Markdown>{hint.text}</Markdown></div>
 }
 
 export function Hints({hints} : {hints: GameHint[]}) {
diff --git a/client/src/components/infoview/infoview.css b/client/src/components/infoview/infoview.css
index 650a679..f90c0d3 100644
--- a/client/src/components/infoview/infoview.css
+++ b/client/src/components/infoview/infoview.css
@@ -4,9 +4,9 @@
   padding: 5px 10px;
   border-radius: 3px 3px 3px 3px;
 }
-.message.information {
-  color: #059;
-  background-color: #BEF;
+.message.info {
+  /* color: #059; */
+  background-color: #DDF6FF;
 }
 .message.warning {
   color: #9F6000;
diff --git a/client/src/components/infoview/main.tsx b/client/src/components/infoview/main.tsx
index dcb0ec7..39075bd 100644
--- a/client/src/components/infoview/main.tsx
+++ b/client/src/components/infoview/main.tsx
@@ -18,11 +18,13 @@ import { EditorContext, ConfigContext, ProgressContext, VersionContext } from '.
 import { WithRpcSessions } from '../../../../node_modules/lean4-infoview/src/infoview/rpcSessions';
 import { ServerVersion } from '../../../../node_modules/lean4-infoview/src/infoview/serverVersion';
 import { useAppDispatch, useAppSelector } from '../../hooks';
-import { codeEdited, levelCompleted, selectCompleted } from '../../state/progress';
+import { levelCompleted, selectCompleted } from '../../state/progress';
+import { GameIdContext } from '../../App';
 
 
 export function Main(props: {world: string, level: number}) {
     const ec = React.useContext(EditorContext);
+    const gameId = React.useContext(GameIdContext)
 
     const dispatch = useAppDispatch()
 
@@ -33,13 +35,13 @@ export function Main(props: {world: string, level: number}) {
 
             if (ec.events.changedCursorLocation.current &&
                 ec.events.changedCursorLocation.current.uri === params.uri) {
-                dispatch(levelCompleted({world: props.world, level: props.level}))
+                dispatch(levelCompleted({game: gameId, world: props.world, level: props.level}))
             }
         },
         []
     );
 
-    const completed = useAppSelector(selectCompleted(props.world, props.level))
+    const completed = useAppSelector(selectCompleted(gameId, props.world, props.level))
 
     /* Set up updates to the global infoview state on editor events. */
     const config = useEventResult(ec.events.changedInfoviewConfig) ?? defaultInfoviewConfig;
diff --git a/client/src/components/welcome.css b/client/src/components/welcome.css
index 849f441..8e457a2 100644
--- a/client/src/components/welcome.css
+++ b/client/src/components/welcome.css
@@ -1,12 +1,191 @@
 
-svg .world-circle {
+/* svg .world-circle {
   fill: var(--clr-primary)
+} */
+
+.welcome {
+  height: 100%;
+  flex: 1;
+  min-height: 0;
+  display: flex;
+}
+
+.app-content {
+  height: 100%
+}
+
+.welcome .column {
+  height: 100%;
+  overflow: auto;
+}
+
+.welcome-text {
+  padding: 20px;
+}
+
+h1 {
+  font-size: 2em;
+  margin: .67em 0;
+}
+
+h2 {
+  font-size: 1.5em;
+}
+
+h3 {
+  font-size: 1.3em;
+}
+
+h4 {
+  font-size: 1.1em;
+  font-style: italic;
+}
+
+h5, h6 {
+  font-size: 1em;
+  font-style: italic;
+}
+
+/***************/
+/* SVG Graphic */
+/***************/
+
+svg .world-title-wrapper {
+  overflow: auto;
+}
+
+svg .world-title-wrapper div {
+  width: 100%;
+  height: 100%;
+}
+
+svg .world-title-wrapper div {
+  display: flex;
+  align-items:center;
+  justify-content:center;
+  overflow: visible;
+
 }
 
-svg .world-name {
-  fill: white;
-  font-size: 2px;
+svg .world-title {
   font-weight: 500;
-  text-anchor: middle;
-  dominant-baseline: middle;
+  color: white;
+  margin: 0;
+  padding: 0;
+}
+
+/******************/
+/* Privacy Button */
+/******************/
+
+.privacy {
+  width: 40px;
+  height: 40px;
+  font-size: 25px;
+  border-radius: 20px;
+  position: absolute;
+  right: 10px;
+  bottom: 10px;
+  display: flex;
+  align-items:center;
+  justify-content:center;
+  color: #aaa;
+  background-color: #eee;
+  cursor: pointer;
+}
+
+.privacy p {
+  position: absolute;
+  color: #888;
+  bottom: 1.5px;
+  font-size: 6px;
+}
+
+.privacy .p1 {
+  transform: rotate(50deg);
+  left: 1.5px;
+}
+
+.privacy .p2 {
+  transform: rotate(-50deg);
+  right: 1.5px;
+}
+
+/*****************/
+/* Privacy Popup */
+/*****************/
+
+.modal-wrapper {
+  position: fixed;
+  top: 0;
+  right: 0;
+  bottom: 0;
+  left: 0;
+  padding: 0;
+}
+
+.modal-backdrop {
+  position: fixed;
+  top: 0;
+  right: 0;
+  bottom: 0;
+  left: 0;
+  background: rgba(0, 0, 0, 0.25);
+  z-index: 2;
+}
+
+.modal h2 {
+  text-align: center;
+}
+
+.modal {
+  position: absolute;
+  top: 50%;
+  left: 50%;
+  transform: translate(-50%, -50%);
+  min-width: 50%;
+  max-width: 60ch;
+  background: #fff;
+  z-index: 3;
+  padding: 2em;
+  border-radius: 1em;
+  text-align: left;
+  color: var(--vscode-breadcrumb-foreground);
+}
+
+.modal input[type="text"] {
+  width: 100%;
+}
+
+.modal .form-error {
+  color: #a00;
+  font-weight: bold;
+}
+
+.modal input[type="submit"] {
+  border: none;
+  color: var(--vscode-button-foreground);
+  background: var(--vscode-button-background);
+  cursor: pointer;
+  padding: .5em 1em;
+  border-radius: .2em;
+  display: block;
+  margin: 1em auto;
+}
+
+.modal-close {
+  float: right;
+  scale: 2;
+  color: var(--vscode-breadcrumb-foreground);
+  cursor: pointer;
+}
+
+.modal-close:hover {
+  float: right;
+  scale: 2;
+  color: var(--vscode-breadcrumb-focusForeground);
+}
+
+.modal table {
+  width: 100%;
 }
diff --git a/client/src/connection.ts b/client/src/connection.ts
index f25b4ca..2d630ac 100644
--- a/client/src/connection.ts
+++ b/client/src/connection.ts
@@ -6,12 +6,17 @@ import { useState } from 'react';
 
 
 export class Connection {
-  private leanClient = null
-
-  getLeanClient(): LeanClient {
-    if (this.leanClient === null) {
-      const socketUrl = ((window.location.protocol === "https:") ? "wss://" : "ws://") + window.location.host + '/websocket/'
+  private game: string = undefined // We only keep a connection to a single game at a time
+  private leanClient: LeanClient = null
 
+  getLeanClient(game): LeanClient {
+    if (this.game !== game) {
+      if (this.leanClient) {
+        this.leanClient.stop() // Stop previous Lean client
+      }
+      this.game = game
+      // Start a new Lean client for the new `gameId`.
+      const socketUrl = ((window.location.protocol === "https:") ? "wss://" : "ws://") + window.location.host + '/websocket/' + game
       const uri = monaco.Uri.parse('file:///')
       this.leanClient = new LeanClient(socketUrl, undefined, uri, () => {})
     }
@@ -22,9 +27,9 @@ export class Connection {
   /** If not already started, starts the Lean client. resolves the returned promise as soon as a
    * Lean client is running.
    */
-  startLeanClient = () => {
+  startLeanClient = (game) => {
     return new Promise<LeanClient>((resolve) => {
-      const leanClient = this.getLeanClient()
+      const leanClient = this.getLeanClient(game)
       if (leanClient.isRunning()) {
         resolve(leanClient)
       } else {
@@ -47,8 +52,8 @@ export const connection = new Connection()
 
 export const ConnectionContext = React.createContext(null);
 
-export const useLeanClient = () => {
-  const leanClient = connection.getLeanClient()
+export const useLeanClient = (gameId) => {
+  const leanClient = connection.getLeanClient(gameId)
   const [leanClientStarted, setLeanClientStarted] = useState(leanClient.isStarted())
 
   React.useEffect(() => {
diff --git a/client/src/index.tsx b/client/src/index.tsx
index d13b276..20f2ac0 100644
--- a/client/src/index.tsx
+++ b/client/src/index.tsx
@@ -13,21 +13,26 @@ import ErrorPage from './ErrorPage';
 import Welcome from './components/Welcome';
 import Level from './components/Level';
 import { monacoSetup } from 'lean4web/client/src/monacoSetup';
+import { redirect } from 'react-router-dom';
 
 monacoSetup()
 
 const router = createHashRouter([
   {
     path: "/",
+    loader: () => redirect("/game/adam")
+  },
+  {
+    path: "/game/:gameId",
     element: <App />,
     errorElement: <ErrorPage />,
     children: [
       {
-        path: "/",
+        path: "/game/:gameId",
         element: <Welcome />,
       },
       {
-        path: "/world/:worldId/level/:levelId",
+        path: "/game/:gameId/world/:worldId/level/:levelId",
         element: <Level />,
       },
     ],
diff --git a/client/src/state/api.ts b/client/src/state/api.ts
index bd5268c..6d93733 100644
--- a/client/src/state/api.ts
+++ b/client/src/state/api.ts
@@ -12,6 +12,7 @@ interface GameInfo {
 
 export interface ComputedInventoryItem {
   name: string,
+  displayName: string,
   category: string,
   disabled: boolean,
   locked: boolean
@@ -31,18 +32,19 @@ interface LevelInfo {
 
 interface Doc {
   name: string,
+  displayName: string,
   text: string
 }
 
 
 const customBaseQuery = async (
-  args : {method: string, params?: any},
+  args : {game: string, method: string, params?: any},
   { signal, dispatch, getState, extra },
   extraOptions
 ) => {
   try {
     const connection : Connection = extra.connection
-    let leanClient = await connection.startLeanClient()
+    let leanClient = await connection.startLeanClient(args.game)
     console.log(`Sending request ${args.method}`)
     let res = await leanClient.sendRequest(args.method, args.params)
     console.log('Received response', res)
@@ -57,14 +59,14 @@ export const apiSlice = createApi({
   reducerPath: 'gameApi',
   baseQuery: customBaseQuery,
   endpoints: (builder) => ({
-    getGameInfo: builder.query<GameInfo, void>({
-      query: () => {return {method: 'info', params: {}}},
+    getGameInfo: builder.query<GameInfo, {game: string}>({
+      query: ({game}) => {return {game, method: 'info', params: {}}},
     }),
-    loadLevel: builder.query<LevelInfo, {world: string, level: number}>({
-      query: ({world, level}) => {return {method: "loadLevel", params: {world, level}}},
+    loadLevel: builder.query<LevelInfo, {game: string, world: string, level: number}>({
+      query: ({game, world, level}) => {return {game, method: "loadLevel", params: {world, level}}},
     }),
-    loadDoc: builder.query<Doc, {name: string, type: "lemma"|"tactic"}>({
-      query: ({name, type}) => {return {method: "loadDoc", params: {name, type}}},
+    loadDoc: builder.query<Doc, {game: string, name: string, type: "lemma"|"tactic"}>({
+      query: ({game, name, type}) => {return {game, method: "loadDoc", params: {name, type}}},
     }),
   }),
 })
diff --git a/client/src/state/localStorage.ts b/client/src/state/localStorage.ts
index a290d75..729d84d 100644
--- a/client/src/state/localStorage.ts
+++ b/client/src/state/localStorage.ts
@@ -1,4 +1,4 @@
-const KEY = "progress";
+const KEY = "game_progress";
 export function loadState() {
   try {
     const serializedState = localStorage.getItem(KEY);
diff --git a/client/src/state/progress.ts b/client/src/state/progress.ts
index 5512322..3d0a29c 100644
--- a/client/src/state/progress.ts
+++ b/client/src/state/progress.ts
@@ -3,23 +3,32 @@ import type { PayloadAction } from '@reduxjs/toolkit'
 import { loadState } from "./localStorage";
 
 interface ProgressState {
-  level: {[world: string]: {[level: number]: LevelProgressState}}
+  level: {[game: string]: {[world: string]: {[level: number]: LevelProgressState}}}
+}
+interface Selection {
+  selectionStartLineNumber: number,
+  selectionStartColumn: number,
+  positionLineNumber: number
+  positionColumn: number
 }
-
 interface LevelProgressState {
   code: string,
+  selections: Selection[],
   completed: boolean
 }
 
 const initialProgressState = loadState() ?? { level: {} } as ProgressState
 const initalLevelProgressState = {code: "", completed: false} as LevelProgressState
 
-function addLevelProgress(state, action: PayloadAction<{world: string, level: number}>) {
-  if (!state.level[action.payload.world]) {
-    state.level[action.payload.world] = {}
+function addLevelProgress(state, action: PayloadAction<{game: string, world: string, level: number}>) {
+  if (!state.level[action.payload.game]) {
+    state.level[action.payload.game] = {}
+  }
+  if (!state.level[action.payload.game][action.payload.world]) {
+    state.level[action.payload.game][action.payload.world] = {}
   }
-  if (!state.level[action.payload.world][action.payload.level]) {
-    state.level[action.payload.world][action.payload.level] = {...initalLevelProgressState}
+  if (!state.level[action.payload.game][action.payload.world][action.payload.level]) {
+    state.level[action.payload.game][action.payload.world][action.payload.level] = {...initalLevelProgressState}
   }
 }
 
@@ -27,35 +36,46 @@ export const progressSlice = createSlice({
   name: 'progress',
   initialState: initialProgressState,
   reducers: {
-    codeEdited(state, action: PayloadAction<{world: string, level: number, code: string}>) {
+    codeEdited(state, action: PayloadAction<{game: string, world: string, level: number, code: string}>) {
+      addLevelProgress(state, action)
+      state.level[action.payload.game][action.payload.world][action.payload.level].code = action.payload.code
+      state.level[action.payload.game][action.payload.world][action.payload.level].completed = false
+    },
+    changedSelection(state, action: PayloadAction<{game: string, world: string, level: number, selections: Selection[]}>) {
       addLevelProgress(state, action)
-      state.level[action.payload.world][action.payload.level].code = action.payload.code
-      state.level[action.payload.world][action.payload.level].completed = false
+      state.level[action.payload.game][action.payload.world][action.payload.level].selections = action.payload.selections
     },
-    levelCompleted(state, action: PayloadAction<{world: string, level: number}>) {
+    levelCompleted(state, action: PayloadAction<{game: string, world: string, level: number}>) {
       addLevelProgress(state, action)
-      state.level[action.payload.world][action.payload.level].completed = true
+      state.level[action.payload.game][action.payload.world][action.payload.level].completed = true
     },
   }
 })
 
-export function selectLevel(world: string, level: number) {
+export function selectLevel(game: string, world: string, level: number) {
   return (state) =>{
-    if (!state.progress.level[world]) { return initalLevelProgressState }
-    if (!state.progress.level[world][level]) { return initalLevelProgressState }
-    return state.progress.level[world][level]
+    if (!state.progress.level[game]) { return initalLevelProgressState }
+    if (!state.progress.level[game][world]) { return initalLevelProgressState }
+    if (!state.progress.level[game][world][level]) { return initalLevelProgressState }
+    return state.progress.level[game][world][level]
+  }
+}
+
+export function selectCode(game: string, world: string, level: number) {
+  return (state) => {
+    return selectLevel(game, world, level)(state).code
   }
 }
 
-export function selectCode(world: string, level: number) {
+export function selectSelections(game: string, world: string, level: number) {
   return (state) => {
-    return selectLevel(world, level)(state).code
+    return selectLevel(game, world, level)(state).selections
   }
 }
 
-export function selectCompleted(world: string, level: number) {
+export function selectCompleted(game: string, world: string, level: number) {
   return (state) => {
-    return selectLevel(world, level)(state).completed
+    return selectLevel(game, world, level)(state).completed
   }
 }
 
@@ -65,4 +85,4 @@ export function selectProgress() {
   }
 }
 
-export const { codeEdited, levelCompleted } = progressSlice.actions
+export const { changedSelection, codeEdited, levelCompleted } = progressSlice.actions
diff --git a/package-lock.json b/package-lock.json
index 26c2ec9..2e6d55a 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -18,6 +18,7 @@
         "@types/cytoscape": "^3.19.9",
         "@types/react-router-dom": "^5.3.3",
         "cytoscape": "^3.23.0",
+        "cytoscape-elk": "^2.1.0",
         "cytoscape-klay": "^3.1.4",
         "debounce": "^1.2.1",
         "express": "^4.18.2",
@@ -34,6 +35,7 @@
         "remark-gfm": "^3.0.1",
         "remark-math": "^5.1.1",
         "vscode-ws-jsonrpc": "^2.0.1",
+        "web-worker": "^1.2.0",
         "ws": "^8.11.0"
       },
       "devDependencies": {
@@ -4180,6 +4182,17 @@
         "node": ">=0.10"
       }
     },
+    "node_modules/cytoscape-elk": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/cytoscape-elk/-/cytoscape-elk-2.1.0.tgz",
+      "integrity": "sha512-stkKoUTNOqpyP5eMuqatK0EYir2NWGTH+XlY0rxFj0t0HiQPGI4AuSuTPaGbNM1WhVfb0tWJ5TQQ0R0qshACLw==",
+      "dependencies": {
+        "elkjs": "^0.8.1"
+      },
+      "peerDependencies": {
+        "cytoscape": "^3.2.0"
+      }
+    },
     "node_modules/cytoscape-klay": {
       "version": "3.1.4",
       "resolved": "https://registry.npmjs.org/cytoscape-klay/-/cytoscape-klay-3.1.4.tgz",
@@ -4435,6 +4448,11 @@
       "resolved": "https://registry.npmjs.org/electron-to-chromium/-/electron-to-chromium-1.4.286.tgz",
       "integrity": "sha512-Vp3CVhmYpgf4iXNKAucoQUDcCrBQX3XLBtwgFqP9BUXuucgvAV9zWp1kYU7LL9j4++s9O+12cb3wMtN4SJy6UQ=="
     },
+    "node_modules/elkjs": {
+      "version": "0.8.2",
+      "resolved": "https://registry.npmjs.org/elkjs/-/elkjs-0.8.2.tgz",
+      "integrity": "sha512-L6uRgvZTH+4OF5NE/MBbzQx/WYpru1xCBE9respNj6qznEewGUIfhzmm7horWWxbNO2M0WckQypGctR8lH79xQ=="
+    },
     "node_modules/emoji-regex": {
       "version": "8.0.0",
       "resolved": "https://registry.npmjs.org/emoji-regex/-/emoji-regex-8.0.0.tgz",
@@ -9869,6 +9887,11 @@
         "url": "https://github.com/sponsors/wooorm"
       }
     },
+    "node_modules/web-worker": {
+      "version": "1.2.0",
+      "resolved": "https://registry.npmjs.org/web-worker/-/web-worker-1.2.0.tgz",
+      "integrity": "sha512-PgF341avzqyx60neE9DD+XS26MMNMoUQRz9NOZwW32nPQrF6p77f1htcnjBSEV8BGMKZ16choqUG4hyI0Hx7mA=="
+    },
     "node_modules/webpack": {
       "version": "5.75.0",
       "resolved": "https://registry.npmjs.org/webpack/-/webpack-5.75.0.tgz",
diff --git a/package.json b/package.json
index a230586..67cab6b 100644
--- a/package.json
+++ b/package.json
@@ -14,6 +14,7 @@
     "@types/cytoscape": "^3.19.9",
     "@types/react-router-dom": "^5.3.3",
     "cytoscape": "^3.23.0",
+    "cytoscape-elk": "^2.1.0",
     "cytoscape-klay": "^3.1.4",
     "debounce": "^1.2.1",
     "express": "^4.18.2",
@@ -30,6 +31,7 @@
     "remark-gfm": "^3.0.1",
     "remark-math": "^5.1.1",
     "vscode-ws-jsonrpc": "^2.0.1",
+    "web-worker": "^1.2.0",
     "ws": "^8.11.0"
   },
   "devDependencies": {
@@ -56,7 +58,7 @@
   },
   "scripts": {
     "start": "concurrently -n server,client -c blue,green \"npm run start_server\" \"npm run start_client\"",
-    "start_server": "cd server && (cd leanserver && lake build) && (cd testgame && lake exe cache get && lake build)  && NODE_ENV=development nodemon -e mjs --exec \"node ./index.mjs\"",
+    "start_server": "cd server && (cd leanserver && lake build) && (cd adam && lake exe cache get && lake build)  && (cd nng && lake build) && NODE_ENV=development nodemon -e mjs --exec \"node ./index.mjs\"",
     "start_client": "NODE_ENV=development webpack-dev-server --hot",
     "build": "npm run build_server && npm run build_client",
     "build_server": "server/build.sh",
diff --git a/server/testgame/.gitignore b/server/adam/.gitignore
similarity index 100%
rename from server/testgame/.gitignore
rename to server/adam/.gitignore
diff --git a/server/testgame/.vscode/settings.json b/server/adam/.vscode/settings.json
similarity index 100%
rename from server/testgame/.vscode/settings.json
rename to server/adam/.vscode/settings.json
diff --git a/server/adam/Adam.lean b/server/adam/Adam.lean
new file mode 100644
index 0000000..2f5351d
--- /dev/null
+++ b/server/adam/Adam.lean
@@ -0,0 +1,44 @@
+import Adam.Metadata
+
+import Adam.Levels.Proposition
+import Adam.Levels.Implication
+import Adam.Levels.Predicate
+import Adam.Levels.Contradiction
+-- import Adam.Levels.Prime
+import Adam.Levels.Sum
+-- import Adam.Levels.Induction
+
+import Adam.Levels.Numbers
+import Adam.Levels.Inequality
+
+import Adam.Levels.Lean
+import Adam.Levels.SetTheory
+import Adam.Levels.Function
+import Adam.Levels.SetFunction
+import Adam.Levels.LinearAlgebra
+
+
+
+Game "Adam"
+Title "Lean 4 game"
+Introduction
+"
+"
+
+Conclusion
+"Fertig!"
+
+
+Path Proposition → Implication → Predicate → Predicate → Contradiction → Sum → Lean
+Path Predicate → Inequality → Sum
+-- Path Inequality → Prime
+-- Path Sum → Inequality -- → Induction
+
+Path Lean → SetTheory → SetTheory2 → SetFunction → Module
+Path Lean → Function → SetFunction
+
+
+Path SetTheory2 → Numbers
+Path Module → Basis → Module2
+
+MakeGame
diff --git a/server/testgame/TestGame/HelperTools.lean b/server/adam/Adam/HelperTools.lean
similarity index 100%
rename from server/testgame/TestGame/HelperTools.lean
rename to server/adam/Adam/HelperTools.lean
diff --git a/server/adam/Adam/LemmaDocs.lean b/server/adam/Adam/LemmaDocs.lean
new file mode 100644
index 0000000..2166bd9
--- /dev/null
+++ b/server/adam/Adam/LemmaDocs.lean
@@ -0,0 +1,514 @@
+import GameServer.Commands
+
+-- Wird im Level "Implication 11" ohne Beweis angenommen.
+LemmaDoc not_not as "not_not" in "Logic"
+"
+`not_not {A : Prop} : ¬¬A ↔ A`
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `Classical`
+* Minimal Import: `Std.Logic`
+* Mathlib Doc: [#not_not](https://leanprover-community.github.io/mathlib4_docs/Std/Logic.html#Classical.not_not)
+"
+
+-- Wird im Level "Implication 10" ohne Beweis angenommen.
+LemmaDoc not_or_of_imp as "not_or_of_imp" in "Logic"
+"
+`not_or_of_imp {A B : Prop} : (A → B) → ¬A ∨ B`
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `-`
+* Minimal Import: `Mathlib.Logic.Basic`
+* Mathlib Doc: [#not_or_of_imp](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#not_or_of_imp)
+"
+
+-- Wird im Level "Implication 12" bewiesen.
+LemmaDoc imp_iff_not_or as "imp_iff_not_or" in "Logic"
+"
+`imp_iff_not_or {A B : Prop} : (A → B) ↔ (¬A ∨ B)`
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `-`
+* Minimal Import: `Mathlib.Logic.Basic`
+* Mathlib Doc: [#imp_iff_not_or](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#imp_iff_not_or)
+"
+
+LemmaDoc Nat.succ_pos as "succ_pos" in "Nat"
+"
+`Nat.succ_pos (n : ℕ) : 0 < n.succ`
+
+$n + 1$ ist strikt grösser als Null.
+
+## Eigenschaften
+
+* `simp` Lemma: Nein
+* Namespace: `Nat`
+* Minimal Import: `Mathlib.Init.Prelude`
+* Mathlib Doc: [#Nat.succ_pos](https://leanprover-community.github.io/mathlib4_docs/Init/Prelude.html#Nat.succ_pos)
+"
+
+LemmaDoc Nat.pos_iff_ne_zero as "pos_iff_ne_zero" in "Nat"
+"
+`Nat.pos_iff_ne_zero {n : ℕ} : 0 < n ↔ n ≠ 0`
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Nat`
+* Minimal Import: `Std.Data.Nat.Lemmas`
+* Mathlib Doc: [#Nat.pos_iff_ne_zero](https://leanprover-community.github.io/mathlib4_docs/Std/Data/Nat/Lemmas.html#Nat.pos_iff_ne_zero)
+"
+
+-- TODO: Not minimal description
+LemmaDoc zero_add as "zero_add" in "Addition"
+"
+`zero_add (a : ℕ) : 0 + a = a`
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `-`
+* Import: `Mathlib.Nat.Basic`
+* Mathlib Doc: [#zero_add](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#zero_add)
+"
+
+LemmaDoc add_zero as "add_zero" in "Addition"
+"
+This lemma says `∀ a : ℕ, a + 0 = a`.
+
+## Eigenschaften
+
+* Mathlib Doc"
+
+LemmaDoc add_succ as "add_succ" in "Addition"
+"This lemma says `∀ a b : ℕ, a + succ b = succ (a + b)`.
+
+## Eigenschaften
+
+* Mathlib Doc: [#]()"
+
+LemmaDoc not_forall as "not_forall" in "Logic"
+"
+`not_forall {α : Sort _} {P : α → Prop} : ¬(∀ x, → P x) ↔ ∃ x, ¬P x`
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `-`
+* Minimal Import: `Mathlib.Logic.Basic`
+* Mathlib Doc: [#not_forall](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#not_forall)
+"
+
+LemmaDoc not_exists as "not_exists" in "Logic"
+"
+`not_exists {α : Sort _} {P : α → Prop} : (¬∃ x, P x) ↔ ∀ (x : α), ¬P x.
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `-`
+* Minimal Import: `Std.Logic`
+* Mathlib Doc: [#not_exists](https://leanprover-community.github.io/mathlib4_docs/Std/Logic.html#not_exists)"
+
+LemmaDoc Nat.even_iff_not_odd as "even_iff_not_odd" in "Nat"
+"
+`even_iff_not_odd  {n : ℕ} : Even n ↔ ¬Odd n`
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Nat`
+* Minimal Import: `Mathlib.Data.Nat.Parity`
+* Mathlib Doc: [#Nat.even_iff_not_odd](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Parity.html#Nat.even_iff_not_odd)"
+
+LemmaDoc Nat.odd_iff_not_even as "odd_iff_not_even" in "Nat"
+"
+`Nat.odd_iff_not_even {n : ℕ} : Odd n ↔ ¬Even n`
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `Nat`
+* Minimal Import: `Mathlib.Data.Nat.Parity`
+* Mathlib Doc: [#Nat.odd_iff_not_even](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Parity.html#Nat.odd_iff_not_even)"
+
+LemmaDoc even_square as "even_square" in "Nat"
+"
+`even_square : (n : ℕ), Even n → Even (n ^ 2)`
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* *Nicht in Mathlib*
+"
+
+
+
+
+LemmaDoc Set.mem_univ as "mem_univ" in "Set"
+"
+`Set.mem_univ {α : Type _} (x : α) : x ∈ @univ α`
+
+Jedes Element ist in `univ`, der Menge aller Elemente eines Typs `α`.
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `Set`
+* Minimal Import: `Mathlib.Data.Set.Basic`
+* Mathlib Doc: [#mem_univ](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.mem_univ)
+"
+
+LemmaDoc not_mem_empty as "not_mem_empty" in "Set"
+"
+`Set.not_mem_empty {α : Type _} (x : α) : x ∉ ∅`
+
+Kein Element ist in der leeren Menge.
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Set`
+* Minimal Import: `Mathlib.Data.Set.Basic`
+* Mathlib Doc: [#not_mem_empty](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.not_mem_empty)
+"
+
+LemmaDoc empty_subset as "empty_subset" in "Set"
+"
+`Set.empty_subset {α : Type u} (s : Set α) : ∅ ⊆ s`
+
+## Eigenschaften
+
+* `simp`-Lemma: Ja
+* Namespace: `Set`
+* Minimal Import: `Mathlib.Data.Set.Basic`
+* Mathlib Doc: [#empty_subset](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.empty_subset)
+"
+
+LemmaDoc Subset.antisymm as "Subset.antisymm" in "Set"
+"
+`Set.Subset.antisymm {α : Type u} {a : Set α} {b : Set α} (h₁ : a ⊆ b) (h₂ : b ⊆ a) : a = b`
+
+Zwei Mengen sind identisch, wenn sowohl $A \\subseteq B$ wie auch $B \\subseteq A$.
+## Details
+
+`apply Subset.antisymm` ist eine Möglichkeit Gleichungen von Mengen zu zeigen.
+eine andere ist `ext i`, welches Elementweise funktiniert.
+Siehe auch
+[`#Subset.antisymm_iff`](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm_iff)
+für die Iff-Version.
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Set.Subset`
+* Minimal Import: `Mathlib.Data.Set.Basic`
+* Mathlib Doc: [#Subset.antisymm](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm)
+"
+
+LemmaDoc Subset.antisymm_iff as "Subset.antisymm_iff" in "Set"
+"
+`Set.Subset.antisymm_iff {α : Type u} {a : Set α} {b : Set α} : a = b ↔ a ⊆ b ∧ b ⊆ a`
+
+Zwei Mengen sind identisch, wenn sowohl $A \\subseteq B$ wie auch $B \\subseteq A$.
+
+## Details
+
+`rw [Subset.antisymm_iff]` ist eine Möglichkeit Gleichungen von Mengen zu zeigen.
+eine andere ist `ext i`, welches Elementweise funktiniert.
+Siehe auch
+[`#Subset.antisymm`](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm)
+für eine verwandte Version.
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Set.Subset`
+* Minimal Import: `Mathlib.Data.Set.Basic`
+* Mathlib Doc: [#Subset.antisymm_iff](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm_iff)
+"
+
+
+LemmaDoc Nat.prime_def_lt'' as "prime_def_lt''" in "Nat"
+"
+`Nat.prime_def_lt'' {p : ℕ} :
+Nat.Prime p ↔ 2 ≤ p ∧ ∀ (m : ℕ), m ∣ p → m = 1 ∨ m = p`
+
+Die bekannte Definition einer Primmzahl in `ℕ`: Eine Zahl (`p ≥ 2`) mit genau zwei Teilern.
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Nat`
+* Mathlib Doc: [#Nat.prime_def_lt''](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime.html#Nat.prime_def_lt'')
+"
+
+
+LemmaDoc Finset.sum_add_distrib as "sum_add_distrib" in "Sum"
+"
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Finset`
+* Mathlib Doc: [#Finset.sum_add_distrib](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Basic.html#Finset.sum_add_distrib)
+"
+
+LemmaDoc Fin.sum_univ_castSucc as "sum_univ_castSucc" in "Sum"
+"
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Fin`
+* Mathlib Doc: [#sum_univ_castSucc](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Fin.html#Fin.sum_univ_castSucc)
+"
+
+LemmaDoc Nat.succ_eq_add_one as "succ_eq_add_one" in "Sum"
+"
+
+## Eigenschaften
+
+* `simp`-Lemma: Nein
+* Namespace: `Nat`
+* Mathlib Doc: [#succ_eq_add_one](https://leanprover-community.github.io/mathlib4_docs/Init/Data/Nat/Basic.html#Nat.succ_eq_add_one)
+"
+
+LemmaDoc Nat.zero_eq as "zero_eq" in "Sum"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#zero_eq](https://leanprover-community.github.io/mathlib4_docs/Init/Data/Nat/Basic.html#Nat.zero_eq)
+"
+
+LemmaDoc add_comm as "add_comm" in "Nat"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#add_comm](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#add_comm)
+"
+
+LemmaDoc mul_add as "mul_add" in "Nat"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#mul_add](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#mul_add)
+"
+
+LemmaDoc add_mul as "add_mul" in "Nat"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#add_mul](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#add_mul)
+"
+
+LemmaDoc arithmetic_sum as "arithmetic_sum" in "Sum"
+"
+
+## Eigenschaften
+
+* Not a mathlib lemma.
+"
+
+LemmaDoc add_pow_two as "add_pow_two" in "Nat"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#add_pow_two](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupPower/Ring.html#add_pow_two)
+"
+
+LemmaDoc Finset.sum_comm as "Finset.sum_comm" in "Sum"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#sum_comm](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Basic.html#Finset.sum_comm)
+"
+
+LemmaDoc Function.comp_apply as "Function.comp_apply" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#comp_apply](https://leanprover-community.github.io/mathlib4_docs/Init/Core.html#Function.comp_apply)
+"
+
+LemmaDoc not_le as "not_le" in "Logic"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#not_le](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Algebra/Order.html#not_le)
+"
+
+LemmaDoc if_pos as "if_pos" in "Logic"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#if_pos](https://leanprover-community.github.io/mathlib4_docs/Init/Core.html#if_pos)
+"
+
+LemmaDoc if_neg as "if_neg" in "Logic"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#if_neg](https://leanprover-community.github.io/mathlib4_docs/Init/Core.html#if_neg)
+"
+
+LemmaDoc StrictMono.injective as "StrictMono.injective" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#StrictMono.injective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Monotone/Basic.html#StrictMono.injective)
+"
+
+LemmaDoc StrictMono.add as "StrictMono.add" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#StrictMono.add](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/Monoid/Lemmas.html#StrictMono.add)
+"
+
+LemmaDoc Odd.strictMono_pow as "Odd.strictMono_pow" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#Odd.strictMono_pow](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Parity.html#Odd.strictMono_pow)
+"
+
+LemmaDoc Exists.choose as "Exists.choose" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#Exists.choose](https://leanprover-community.github.io/mathlib4_docs/Std/Logic.html#Exists.choose)
+"
+
+LemmaDoc Exists.choose_spec as "Exists.choose_spec" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#Exists.choose_spec](https://leanprover-community.github.io/mathlib4_docs/Std/Logic.html#Exists.choose_spec)
+"
+LemmaDoc congrArg as "congrArg" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#congrArg](https://leanprover-community.github.io/mathlib4_docs/Init/Prelude.html#congrArg)
+"
+LemmaDoc congrFun as "congrFun" in "Function"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#congrFun](https://leanprover-community.github.io/mathlib4_docs/Init/Prelude.html#congrFun)
+"
+
+LemmaDoc Iff.symm as "Iff.symm" in "Logic"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#Iff.symm](https://leanprover-community.github.io/mathlib4_docs/Init/Core.html#Iff.symm)
+"
+
+
+
+/-! ## Definitions -/
+
+DefinitionDoc Even as "Even"
+"
+`even n` ist definiert als `∃ r, a = 2 * r`.
+Die Definition kann man mit `unfold even at *` einsetzen.
+## Eigenschaften
+
+* Mathlib Doc: [#Even](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Parity.html#Even)"
+
+DefinitionDoc Odd as "Odd"
+"
+`odd n` ist definiert als `∃ r, a = 2 * r + 1`.
+Die Definition kann man mit `unfold odd at *` einsetzen.
+
+* Mathlib Doc: [Odd](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Parity.html#Odd)"
+
+DefinitionDoc Injective as "Injective"
+"
+`Injective f` ist definiert als
+
+```
+∀ a b, f a = f b → a = b
+```
+definiert.
+
+* Mathlib Doc: [Injective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.Injective)"
+
+DefinitionDoc Surjective as "Surjective"
+"
+`Surjective f` ist definiert als
+
+```
+∀ a, (∃ b, f a = b)
+```
+
+* Mathlib Doc: [Surjective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.Surjective)"
+
+DefinitionDoc Bijective as "Bijective"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#Bijective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.Bijective)
+"
+
+DefinitionDoc LeftInverse as "LeftInverse"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#LeftInverse](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.LeftInverse)
+"
+
+DefinitionDoc RightInverse as "RightInverse"
+"
+
+## Eigenschaften
+
+* Mathlib Doc: [#RightInverse](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Logic.html#RightInverse)
+"
+
+DefinitionDoc StrictMono as "StrictMono"
+"
+`StrictMono f` ist definiert als
+
+```
+∀ a b, a < b → f a < f b
+```
+
+## Eigenschaften
+
+* Mathlib Doc: [#StrictMono](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Monotone/Basic.html#StrictMono)
+
+"
+
+DefinitionDoc Symbol.Subset as "⊆" "
+
+Auf Mengen (`Set`) ist `A ⊆ B` als `∀x, x ∈ A → x ∈ B` implementiert.
+"
diff --git a/server/adam/Adam/Levels/Contradiction.lean b/server/adam/Adam/Levels/Contradiction.lean
new file mode 100644
index 0000000..a7cdde7
--- /dev/null
+++ b/server/adam/Adam/Levels/Contradiction.lean
@@ -0,0 +1,16 @@
+import Adam.Levels.Contradiction.L01_Have
+import Adam.Levels.Contradiction.L02_Suffices
+import Adam.Levels.Contradiction.L03_ByContra
+import Adam.Levels.Contradiction.L04_ByContra
+import Adam.Levels.Contradiction.L05_Contrapose
+import Adam.Levels.Contradiction.L06_Summary
+
+Game "Adam"
+World "Contradiction"
+Title "Widerspruch"
+
+Introduction "
+Ihr begebt euch auf die Suche nach *Oddeus*. Nach etwas rumfragen, kommt ihr tatsächlich an
+eine Dornenfestung und nachdem ihr erklärt habt, wer ihr seit, werdet ihr auf eine Audienz
+gebeten.
+"
diff --git a/server/testgame/TestGame/Levels/Contradiction/L01_Have.lean b/server/adam/Adam/Levels/Contradiction/L01_Have.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Contradiction/L01_Have.lean
rename to server/adam/Adam/Levels/Contradiction/L01_Have.lean
index e80a472..01d4aa3 100644
--- a/server/testgame/TestGame/Levels/Contradiction/L01_Have.lean
+++ b/server/adam/Adam/Levels/Contradiction/L01_Have.lean
@@ -1,13 +1,13 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Contradiction"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/Contradiction/L02_Suffices.lean b/server/adam/Adam/Levels/Contradiction/L02_Suffices.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Contradiction/L02_Suffices.lean
rename to server/adam/Adam/Levels/Contradiction/L02_Suffices.lean
index 5480fe4..ac8f762 100644
--- a/server/testgame/TestGame/Levels/Contradiction/L02_Suffices.lean
+++ b/server/adam/Adam/Levels/Contradiction/L02_Suffices.lean
@@ -1,13 +1,13 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Contradiction"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/Contradiction/L03_ByContra.lean b/server/adam/Adam/Levels/Contradiction/L03_ByContra.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Contradiction/L03_ByContra.lean
rename to server/adam/Adam/Levels/Contradiction/L03_ByContra.lean
index c9e4013..4a178bf 100644
--- a/server/testgame/TestGame/Levels/Contradiction/L03_ByContra.lean
+++ b/server/adam/Adam/Levels/Contradiction/L03_ByContra.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 import Mathlib.Tactic.Contrapose
@@ -6,9 +6,9 @@ import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 import Mathlib
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Contradiction"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/Contradiction/L04_ByContra.lean b/server/adam/Adam/Levels/Contradiction/L04_ByContra.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Contradiction/L04_ByContra.lean
rename to server/adam/Adam/Levels/Contradiction/L04_ByContra.lean
index 769a4cc..f9530cc 100644
--- a/server/testgame/TestGame/Levels/Contradiction/L04_ByContra.lean
+++ b/server/adam/Adam/Levels/Contradiction/L04_ByContra.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 import Mathlib.Tactic.Contrapose
@@ -6,9 +6,9 @@ import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 import Mathlib
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Contradiction"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/Contradiction/L05_Contrapose.lean b/server/adam/Adam/Levels/Contradiction/L05_Contrapose.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Contradiction/L05_Contrapose.lean
rename to server/adam/Adam/Levels/Contradiction/L05_Contrapose.lean
index 6377dec..e2df673 100644
--- a/server/testgame/TestGame/Levels/Contradiction/L05_Contrapose.lean
+++ b/server/adam/Adam/Levels/Contradiction/L05_Contrapose.lean
@@ -1,12 +1,12 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Contradiction"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/Contradiction/L06_Summary.lean b/server/adam/Adam/Levels/Contradiction/L06_Summary.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Contradiction/L06_Summary.lean
rename to server/adam/Adam/Levels/Contradiction/L06_Summary.lean
index 64693b0..1e32524 100644
--- a/server/testgame/TestGame/Levels/Contradiction/L06_Summary.lean
+++ b/server/adam/Adam/Levels/Contradiction/L06_Summary.lean
@@ -1,12 +1,12 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Contradiction"
 Level 6
 
diff --git a/server/adam/Adam/Levels/Function.lean b/server/adam/Adam/Levels/Function.lean
new file mode 100644
index 0000000..91a8bbe
--- /dev/null
+++ b/server/adam/Adam/Levels/Function.lean
@@ -0,0 +1,24 @@
+import Adam.Levels.Function.L01_Function
+import Adam.Levels.Function.L02_Let
+import Adam.Levels.Function.L03_Piecewise
+import Adam.Levels.Function.L04_Injective
+import Adam.Levels.Function.L05_Injective
+import Adam.Levels.Function.L06_Injective
+import Adam.Levels.Function.L07_Surjective
+import Adam.Levels.Function.L08_Bijective
+import Adam.Levels.Function.L09_Inverse
+import Adam.Levels.Function.L11_Inverse
+
+Game "Adam"
+World "Function"
+Title "Abbildungen"
+
+Introduction "
+Auf der Suche nach dem Buch der Urbilder landet ihr auf einem kleinen Mond, der bis auf
+eine Insel komplett mit Wasser bedeckt zu sein scheint.
+
+Auf der Insel seht ihr verschiedene große und kleine Behausungen, manche aus Stroh und Holz,
+vereinzelte aus Lehm.
+
+Planlos geht ihr zum ersten Haus bei dem jemand vorne außen sitzt.
+"
diff --git a/server/testgame/TestGame/Levels/Function/L01_Function.lean b/server/adam/Adam/Levels/Function/L01_Function.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Function/L01_Function.lean
rename to server/adam/Adam/Levels/Function/L01_Function.lean
index 1bce9e1..52607f9 100644
--- a/server/testgame/TestGame/Levels/Function/L01_Function.lean
+++ b/server/adam/Adam/Levels/Function/L01_Function.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/Function/L02_Let.lean b/server/adam/Adam/Levels/Function/L02_Let.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/Function/L02_Let.lean
rename to server/adam/Adam/Levels/Function/L02_Let.lean
index b996425..80c95c6 100644
--- a/server/testgame/TestGame/Levels/Function/L02_Let.lean
+++ b/server/adam/Adam/Levels/Function/L02_Let.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/Function/L03_Piecewise.lean b/server/adam/Adam/Levels/Function/L03_Piecewise.lean
similarity index 99%
rename from server/testgame/TestGame/Levels/Function/L03_Piecewise.lean
rename to server/adam/Adam/Levels/Function/L03_Piecewise.lean
index 8c1615b..591a081 100644
--- a/server/testgame/TestGame/Levels/Function/L03_Piecewise.lean
+++ b/server/adam/Adam/Levels/Function/L03_Piecewise.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/Function/L04_Injective.lean b/server/adam/Adam/Levels/Function/L04_Injective.lean
similarity index 95%
rename from server/testgame/TestGame/Levels/Function/L04_Injective.lean
rename to server/adam/Adam/Levels/Function/L04_Injective.lean
index 0946ab4..b21a7fc 100644
--- a/server/testgame/TestGame/Levels/Function/L04_Injective.lean
+++ b/server/adam/Adam/Levels/Function/L04_Injective.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/Function/L05_Injective.lean b/server/adam/Adam/Levels/Function/L05_Injective.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/Function/L05_Injective.lean
rename to server/adam/Adam/Levels/Function/L05_Injective.lean
index 48f0172..17bf39f 100644
--- a/server/testgame/TestGame/Levels/Function/L05_Injective.lean
+++ b/server/adam/Adam/Levels/Function/L05_Injective.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/Function/L06_Injective.lean b/server/adam/Adam/Levels/Function/L06_Injective.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Function/L06_Injective.lean
rename to server/adam/Adam/Levels/Function/L06_Injective.lean
index 4e61007..2335749 100644
--- a/server/testgame/TestGame/Levels/Function/L06_Injective.lean
+++ b/server/adam/Adam/Levels/Function/L06_Injective.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 6
 
diff --git a/server/testgame/TestGame/Levels/Function/L07_Surjective.lean b/server/adam/Adam/Levels/Function/L07_Surjective.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Function/L07_Surjective.lean
rename to server/adam/Adam/Levels/Function/L07_Surjective.lean
index 27906d8..7f493b3 100644
--- a/server/testgame/TestGame/Levels/Function/L07_Surjective.lean
+++ b/server/adam/Adam/Levels/Function/L07_Surjective.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 7
 
diff --git a/server/testgame/TestGame/Levels/Function/L08_Bijective.lean b/server/adam/Adam/Levels/Function/L08_Bijective.lean
similarity index 89%
rename from server/testgame/TestGame/Levels/Function/L08_Bijective.lean
rename to server/adam/Adam/Levels/Function/L08_Bijective.lean
index 1fc8135..98aec98 100644
--- a/server/testgame/TestGame/Levels/Function/L08_Bijective.lean
+++ b/server/adam/Adam/Levels/Function/L08_Bijective.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 8
 
@@ -33,6 +33,6 @@ Hint : Bijective (fun (n : ℤ) ↦ n + 1) =>
 
 Conclusion
 "Zufrieden drückt euch der Gelehrte eine neue Fackel in die Hand und
-zeigt euch den Weg nach draussen."
+zeigt euch den Weg nach draußen."
 
 NewDefinition Bijective
diff --git a/server/testgame/TestGame/Levels/Function/L09_Inverse.lean b/server/adam/Adam/Levels/Function/L09_Inverse.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Function/L09_Inverse.lean
rename to server/adam/Adam/Levels/Function/L09_Inverse.lean
index 548d01e..120ccbd 100644
--- a/server/testgame/TestGame/Levels/Function/L09_Inverse.lean
+++ b/server/adam/Adam/Levels/Function/L09_Inverse.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 9
 
diff --git a/server/testgame/TestGame/Levels/Function/L11_Inverse.lean b/server/adam/Adam/Levels/Function/L11_Inverse.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/Function/L11_Inverse.lean
rename to server/adam/Adam/Levels/Function/L11_Inverse.lean
index 14ac036..f6b0c68 100644
--- a/server/testgame/TestGame/Levels/Function/L11_Inverse.lean
+++ b/server/adam/Adam/Levels/Function/L11_Inverse.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 10
 
diff --git a/server/testgame/TestGame/Levels/Implication.lean b/server/adam/Adam/Levels/Implication.lean
similarity index 51%
rename from server/testgame/TestGame/Levels/Implication.lean
rename to server/adam/Adam/Levels/Implication.lean
index 0d06e71..6b77705 100644
--- a/server/testgame/TestGame/Levels/Implication.lean
+++ b/server/adam/Adam/Levels/Implication.lean
@@ -1,18 +1,18 @@
-import TestGame.Levels.Implication.L01_Intro
-import TestGame.Levels.Implication.L02_Revert
-import TestGame.Levels.Implication.L03_Apply
-import TestGame.Levels.Implication.L04_Apply
-import TestGame.Levels.Implication.L05_Apply
-import TestGame.Levels.Implication.L06_Iff
-import TestGame.Levels.Implication.L07_Rw
-import TestGame.Levels.Implication.L08_Iff
-import TestGame.Levels.Implication.L09_Iff
-import TestGame.Levels.Implication.L10_Apply
-import TestGame.Levels.Implication.L11_ByCases
-import TestGame.Levels.Implication.L12_Rw
-import TestGame.Levels.Implication.L13_Summary
+import Adam.Levels.Implication.L01_Intro
+import Adam.Levels.Implication.L02_Revert
+import Adam.Levels.Implication.L03_Apply
+import Adam.Levels.Implication.L04_Apply
+import Adam.Levels.Implication.L05_Apply
+import Adam.Levels.Implication.L06_Iff
+import Adam.Levels.Implication.L07_Rw
+import Adam.Levels.Implication.L08_Iff
+import Adam.Levels.Implication.L09_Iff
+import Adam.Levels.Implication.L10_Apply
+import Adam.Levels.Implication.L11_ByCases
+import Adam.Levels.Implication.L12_Rw
+import Adam.Levels.Implication.L13_Summary
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Title "Aussagenlogik 2"
 
@@ -28,7 +28,7 @@ aber niemand von den Einwohnern wusste was davon...
 erzählen…
 
 Und damit leitet Robo den Landeanflug ein. Implis scheint ein riesiger Tagbau zu sein auf
-dem nach allem möglichen gegraben wird. Überall seht ihr Förderbänder kreuz und queer.
+dem nach allem möglichen gegraben wird. Überall seht ihr Förderbänder kreuz und quer.
 
 Das Operationsteam begrüsst euch freundlich und lädt zum Essen im Kommandoturm.
 "
diff --git a/server/testgame/TestGame/Levels/Implication/L01_Intro.lean b/server/adam/Adam/Levels/Implication/L01_Intro.lean
similarity index 82%
rename from server/testgame/TestGame/Levels/Implication/L01_Intro.lean
rename to server/adam/Adam/Levels/Implication/L01_Intro.lean
index 7a60817..97fef55 100644
--- a/server/testgame/TestGame/Levels/Implication/L01_Intro.lean
+++ b/server/adam/Adam/Levels/Implication/L01_Intro.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Tauto
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 1
 
@@ -18,7 +18,8 @@ Statement (A B : Prop) (hb : B) : A → (A ∧ B) := by
   Hint "**Du**: Einen Moment, das ist eine Implikation (`\\to`),
   also `A` impliziert `A und B`, soweit so gut, also eine Tautologie.
 
-  **Robo**: Die scheinen hier `tauto` auch nicht zu verstehen.
+  **Robo**: Du hast recht, eigentlich könnte man `tauto` sagen,
+  aber das scheinen die hier tauto nicht zu verstehen.
   Implikationen kannst du aber mit `intro h` angehen."
   intro hA
   Hint "**Du**: Jetzt habe ich also angenommen, dass `A` wahr ist und muss `A ∧ B` zeigen,
diff --git a/server/testgame/TestGame/Levels/Implication/L02_Revert.lean b/server/adam/Adam/Levels/Implication/L02_Revert.lean
similarity index 95%
rename from server/testgame/TestGame/Levels/Implication/L02_Revert.lean
rename to server/adam/Adam/Levels/Implication/L02_Revert.lean
index f05a5c9..5345c60 100644
--- a/server/testgame/TestGame/Levels/Implication/L02_Revert.lean
+++ b/server/adam/Adam/Levels/Implication/L02_Revert.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/Implication/L03_Apply.lean b/server/adam/Adam/Levels/Implication/L03_Apply.lean
similarity index 60%
rename from server/testgame/TestGame/Levels/Implication/L03_Apply.lean
rename to server/adam/Adam/Levels/Implication/L03_Apply.lean
index 5d917f4..30eb21f 100644
--- a/server/testgame/TestGame/Levels/Implication/L03_Apply.lean
+++ b/server/adam/Adam/Levels/Implication/L03_Apply.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 3
 
@@ -11,17 +11,10 @@ Introduction
 "
 Sein Kollege zieht eine Linie unter deinen Beweis, schreibt ein durchgestrichenes ~`revert`~
 hin und gibt dir das Blatt wieder.
-`revert` ist aber nur selten der richtige Weg.
-
-Im vorigen Beispiel würde man besser die Implikation $A \\Rightarrow B$ *anwenden*, also
-sagen \"Es genügt $A$ zu zeigen, denn $A \\Rightarrow B$\" und danach $A$ beweisen.
-
-Wenn man eine Implikation `(g : A → B)` in den Annahmen hat, bei welcher die Konsequenz
-(also $B$) mit dem Goal übereinstimmt, kann man `apply g` genau dies machen.
 "
 
 Statement (A B : Prop) (hA : A) (h : A → B) : B := by
-  Hint "**Robo**: Du hast natürlich recht, normalerweise ist es viel schöner mit
+  Hint "**Robo**: Da hat er natürlich recht, normalerweise ist es viel schöner mit
   `apply {h}` die Implikation anzuwenden."
   apply h
   Hint "**Du**: Und jetzt genügt es also `A` zu zeigen."
diff --git a/server/testgame/TestGame/Levels/Implication/L04_Apply.lean b/server/adam/Adam/Levels/Implication/L04_Apply.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Implication/L04_Apply.lean
rename to server/adam/Adam/Levels/Implication/L04_Apply.lean
index 1d4a7a9..bef022c 100644
--- a/server/testgame/TestGame/Levels/Implication/L04_Apply.lean
+++ b/server/adam/Adam/Levels/Implication/L04_Apply.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/Implication/L05_Apply.lean b/server/adam/Adam/Levels/Implication/L05_Apply.lean
similarity index 92%
rename from server/testgame/TestGame/Levels/Implication/L05_Apply.lean
rename to server/adam/Adam/Levels/Implication/L05_Apply.lean
index 78b48cc..ef92b93 100644
--- a/server/testgame/TestGame/Levels/Implication/L05_Apply.lean
+++ b/server/adam/Adam/Levels/Implication/L05_Apply.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 5
 
@@ -8,7 +8,7 @@ Title "Implikation"
 
 Introduction
 "
-Selbstsicher folgt ihr den Anweisungen und geht nach draussen zum
+Selbstsicher folgt ihr den Anweisungen und geht nach draußen zum
 defekten Kontrollelement. Dieses zeigt ein kompliziertes Diagram:
 $$
 \\begin{CD}
diff --git a/server/testgame/TestGame/Levels/Implication/L06_Iff.lean b/server/adam/Adam/Levels/Implication/L06_Iff.lean
similarity index 89%
rename from server/testgame/TestGame/Levels/Implication/L06_Iff.lean
rename to server/adam/Adam/Levels/Implication/L06_Iff.lean
index 7f5ea41..3941d32 100644
--- a/server/testgame/TestGame/Levels/Implication/L06_Iff.lean
+++ b/server/adam/Adam/Levels/Implication/L06_Iff.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 6
 
@@ -37,7 +37,7 @@ hier bei `(h : A ↔ B)` heissen sie `h.mp` und `h.mpr`.
 **Operationsleiter**: \"Modulo Ponens\" ist ein lokaler Begriff hier,
 aber das ist doch nicht wichtig.
 
-**Robo**: Und das \"r\" in `mpr` stünde für \"reverse\" weils die Rückrichtung ist.
+**Robo**: Und das \"r\" in `mpr` stünde für \"reverse\" weil's die Rückrichtung ist.
 "
 
 NewTactic constructor
diff --git a/server/testgame/TestGame/Levels/Implication/L07_Rw.lean b/server/adam/Adam/Levels/Implication/L07_Rw.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Implication/L07_Rw.lean
rename to server/adam/Adam/Levels/Implication/L07_Rw.lean
index a224432..dc1fa5d 100644
--- a/server/testgame/TestGame/Levels/Implication/L07_Rw.lean
+++ b/server/adam/Adam/Levels/Implication/L07_Rw.lean
@@ -1,9 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Init.Data.ToString
 -- #check List UInt8
 
-Game "TestGame"
+set_option tactic.hygienic false
+
+Game "Adam"
 World "Implication"
 Level 7
 
diff --git a/server/testgame/TestGame/Levels/Implication/L08_Iff.lean b/server/adam/Adam/Levels/Implication/L08_Iff.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Implication/L08_Iff.lean
rename to server/adam/Adam/Levels/Implication/L08_Iff.lean
index 8801210..0cd443d 100644
--- a/server/testgame/TestGame/Levels/Implication/L08_Iff.lean
+++ b/server/adam/Adam/Levels/Implication/L08_Iff.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 8
 
diff --git a/server/testgame/TestGame/Levels/Implication/L09_Iff.lean b/server/adam/Adam/Levels/Implication/L09_Iff.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Implication/L09_Iff.lean
rename to server/adam/Adam/Levels/Implication/L09_Iff.lean
index daede52..60835df 100644
--- a/server/testgame/TestGame/Levels/Implication/L09_Iff.lean
+++ b/server/adam/Adam/Levels/Implication/L09_Iff.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Cases
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 9
 
diff --git a/server/testgame/TestGame/Levels/Implication/L10_Apply.lean b/server/adam/Adam/Levels/Implication/L10_Apply.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Implication/L10_Apply.lean
rename to server/adam/Adam/Levels/Implication/L10_Apply.lean
index 8905f6f..5e47099 100644
--- a/server/testgame/TestGame/Levels/Implication/L10_Apply.lean
+++ b/server/adam/Adam/Levels/Implication/L10_Apply.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Cases
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 10
 
diff --git a/server/testgame/TestGame/Levels/Implication/L11_ByCases.lean b/server/adam/Adam/Levels/Implication/L11_ByCases.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Implication/L11_ByCases.lean
rename to server/adam/Adam/Levels/Implication/L11_ByCases.lean
index 7493335..d5048b4 100644
--- a/server/testgame/TestGame/Levels/Implication/L11_ByCases.lean
+++ b/server/adam/Adam/Levels/Implication/L11_ByCases.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Cases
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 11
 
diff --git a/server/testgame/TestGame/Levels/Implication/L12_Rw.lean b/server/adam/Adam/Levels/Implication/L12_Rw.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Implication/L12_Rw.lean
rename to server/adam/Adam/Levels/Implication/L12_Rw.lean
index ed9683a..5685c3a 100644
--- a/server/testgame/TestGame/Levels/Implication/L12_Rw.lean
+++ b/server/adam/Adam/Levels/Implication/L12_Rw.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Cases
 import Mathlib.Logic.Basic
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 12
 
diff --git a/server/testgame/TestGame/Levels/Implication/L13_Summary.lean b/server/adam/Adam/Levels/Implication/L13_Summary.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/Implication/L13_Summary.lean
rename to server/adam/Adam/Levels/Implication/L13_Summary.lean
index 6de3e35..0e86aad 100644
--- a/server/testgame/TestGame/Levels/Implication/L13_Summary.lean
+++ b/server/adam/Adam/Levels/Implication/L13_Summary.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 import Mathlib
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 13
 
diff --git a/server/adam/Adam/Levels/Induction.lean b/server/adam/Adam/Levels/Induction.lean
new file mode 100644
index 0000000..5e77bb6
--- /dev/null
+++ b/server/adam/Adam/Levels/Induction.lean
@@ -0,0 +1,5 @@
+import Adam.Levels.Induction.L01_Induction
+
+Game "Adam"
+World "Induction"
+Title "Übungen Induktions"
diff --git a/server/testgame/TestGame/Levels/Induction/L01_Induction.lean b/server/adam/Adam/Levels/Induction/L01_Induction.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Induction/L01_Induction.lean
rename to server/adam/Adam/Levels/Induction/L01_Induction.lean
index f2804b9..66a8473 100644
--- a/server/testgame/TestGame/Levels/Induction/L01_Induction.lean
+++ b/server/adam/Adam/Levels/Induction/L01_Induction.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Induction"
 Level 1
 
diff --git a/server/adam/Adam/Levels/Inequality.lean b/server/adam/Adam/Levels/Inequality.lean
new file mode 100644
index 0000000..d136814
--- /dev/null
+++ b/server/adam/Adam/Levels/Inequality.lean
@@ -0,0 +1,16 @@
+import Adam.Levels.Inequality.L01_LE
+import Adam.Levels.Inequality.L02_Pos
+import Adam.Levels.Inequality.L03_Linarith
+import Adam.Levels.Inequality.L04_Linarith
+
+Game "Adam"
+World "Inequality"
+Title "Ungleichung"
+
+Introduction "
+Später erinnerst du dich gar nicht mehr wo und wann du diese Unterhaltung hattest, geschweige
+denn mit wem. Vielleicht war es ein Traum, oder eine Erscheinung. Vielleicht war es
+auch nur eines Abends über einer Runde Getränke.
+
+Aber auf jedenfall hast du irgendwo gelernt, was du nun weisst.
+"
diff --git a/server/adam/Adam/Levels/Inequality/L01_LE.lean b/server/adam/Adam/Levels/Inequality/L01_LE.lean
new file mode 100644
index 0000000..eaebe8b
--- /dev/null
+++ b/server/adam/Adam/Levels/Inequality/L01_LE.lean
@@ -0,0 +1,34 @@
+import Adam.Metadata
+
+Game "Adam"
+World "Inequality"
+Level 1
+
+Title "Kleinergleich"
+
+Introduction
+"
+*(Gesrpäch)*
+
+**Robo** (*lallend*, oder war's fröhlich proklamierend?):
+…und deshalb sind `≥` und `>` eigentlich nur Notationen für `≤`,
+welches man übrigens `\\le` schreibt, was für Less-Equal (also Kleinergleich) steht…
+
+**Du**: Wir haben's verstanden, man benützt also Standartmässig lieber `≤` und `<`,
+aber damit weiß ich eh nichts anzufangen.
+
+**dritte Person**: Komm schon, das kannst du ja sicher:
+"
+
+Statement
+  (n m : ℕ) : m < n ↔ m.succ ≤ n := by
+  Hint "**Robo**: Du Narr! Das ist doch eine Kuriosität, dass `m < n` auf `ℕ` per Definition
+  als `m + 1 ≤ n` definiert ist!
+
+  **dritte Person**: Du verdirbst den Witz! Ich wollte ihn doch nur testen."
+  rfl
+
+OnlyTactic rfl
+
+Conclusion "**Du**: Ha. ha… Na aber jetzt mal ehrlich, könnt ihr mir ein bisschen mehr
+erzählen?"
diff --git a/server/adam/Adam/Levels/Inequality/L02_Pos.lean b/server/adam/Adam/Levels/Inequality/L02_Pos.lean
new file mode 100644
index 0000000..e328984
--- /dev/null
+++ b/server/adam/Adam/Levels/Inequality/L02_Pos.lean
@@ -0,0 +1,53 @@
+import Adam.Metadata
+
+import Mathlib.Tactic.LibrarySearch
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Inequality"
+Level 2
+
+Title "Kleinergleich"
+
+Introduction
+"
+*weitere Person*: …ich sag dir, eine positive Zahl kann man sowohl mit `0 < n`
+als auch `n ≠ 0` darstellen.
+
+*Robo*: Und da gibts leider keinen Standard dazu.
+
+**weitere Person*: Ja und, da kann man ja einfach mit `Nat.pos_iff_ne_zero`
+wechseln. Wart mal, wieso galt das nochmals…
+"
+
+Statement Nat.pos_iff_ne_zero (n : ℕ) : 0 < n ↔ n ≠ 0 := by
+  Hint "**Robo** (*flüsternd*): Wenn du ein bisschen schwere Maschinerie auffahren willst,
+  um in zu beeindrucken, hab ich was. Mach doch eine Fallunterscheidung ob `n` Null ist
+  oder nicht!
+
+  **Du** (*flüsternd*): Und wie geht das?
+
+  **Robo** (*laut und selbstsicher*): Wir fangen mit `rcases n` an!"
+  rcases n
+  Hint "**Du**: Hmm, das muss man doch vereinfachen können.
+
+  **Robo** (*flüsternd*): Zweiter pompöser Auftritt: sag einfach `simp` und lass das alles
+  automatisch geschehen."
+  simp
+  Hint "**Du**: Und hier fang ich wohl am besten an wie ich das schon kenne."
+  constructor
+  intro
+  simp
+  intro
+  Hint "**Robo**: Warte! Den Rest geb ich dir als Lemma: `Nat.suc_pos`."
+  apply Nat.succ_pos
+
+NewTactic simp
+NewLemma Nat.succ_pos
+DisabledLemma Nat.pos_iff_ne_zero
+
+Conclusion "**Du**: Oh `simp` ist ja echt nicht schlecht…
+
+Die andere Person scheint beeindruckt, hat aber gleichzeitig auch das Bedürfnis, Dich aus
+der Reserve zu locken."
diff --git a/server/adam/Adam/Levels/Inequality/L03_Linarith.lean b/server/adam/Adam/Levels/Inequality/L03_Linarith.lean
new file mode 100644
index 0000000..bec5fdb
--- /dev/null
+++ b/server/adam/Adam/Levels/Inequality/L03_Linarith.lean
@@ -0,0 +1,26 @@
+import Adam.Metadata
+import Mathlib.Tactic.Linarith
+
+Game "Adam"
+World "Inequality"
+Level 3
+
+Title "Linarith"
+
+Introduction
+"
+**dritte Person**: Nah wenn wir so spielen:
+"
+
+Statement (n : ℕ) (h : 2 ≤ n) : n ≠ 0 := by
+  Hint "**Du**: `simp` geht hier nicht, was mir ja auch einläuchtet.
+
+  **Robo**: Ist auch keine Vereinfachung, die du machen willst. Stattdessen,
+  `linarith` kann lineare Gleichungen und Ungleichungen lösen. Das ist das Powertool
+  in der hinsicht."
+  linarith
+
+NewTactic linarith
+NewLemma Nat.pos_iff_ne_zero
+
+Conclusion "**Du**: Naja so beeindruckend war das jetzt auch noch nicht."
diff --git a/server/adam/Adam/Levels/Inequality/L04_Linarith.lean b/server/adam/Adam/Levels/Inequality/L04_Linarith.lean
new file mode 100644
index 0000000..0cb1618
--- /dev/null
+++ b/server/adam/Adam/Levels/Inequality/L04_Linarith.lean
@@ -0,0 +1,29 @@
+import Adam.Metadata
+import Mathlib.Tactic.Linarith
+
+Game "Adam"
+World "Inequality"
+Level 4
+
+Title "Linarith"
+
+Introduction
+"
+**Robo**: Die Taktik kann aber noch viel mehr.
+
+**weitere Person**: Hier, probier mal!
+
+$$
+\\begin{aligned}
+  5 * y &\\le 35 - 2 * x \\\\
+  2 * y &\\le x + 3
+\\end{aligned}
+$$
+"
+
+Statement (x y : ℤ) (h₂ : 5 * y ≤ 35 - 2 * x) (h₃ : 2 * y ≤ x + 3) : y ≤ 5 := by
+  linarith
+
+Conclusion "**Du**: Boah, das ist schon gar nicht schlecht.
+
+Und damit endet auch Deine Erinnerung und wer weiss was du anschließend gemacht hast…"
diff --git a/server/testgame/TestGame/Levels/Inequality/T_Induction.lean b/server/adam/Adam/Levels/Inequality/T_Induction.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Inequality/T_Induction.lean
rename to server/adam/Adam/Levels/Inequality/T_Induction.lean
index a393275..0d0830b 100644
--- a/server/testgame/TestGame/Levels/Inequality/T_Induction.lean
+++ b/server/adam/Adam/Levels/Inequality/T_Induction.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Inequality"
 Level 1
 
diff --git a/server/adam/Adam/Levels/Lean.lean b/server/adam/Adam/Levels/Lean.lean
new file mode 100644
index 0000000..ff5f672
--- /dev/null
+++ b/server/adam/Adam/Levels/Lean.lean
@@ -0,0 +1,26 @@
+import Adam.Levels.Lean.L01_Type
+import Adam.Levels.Lean.L02_Universe
+import Adam.Levels.Lean.L03_ImplicitArguments
+import Adam.Levels.Lean.L04_InstanceArguments
+
+Game "Adam"
+World "Lean"
+Title "Lean"
+
+Introduction
+"Während ihr weiter durch Täler, über Geröllhalden und zwischen monumentalen Steintürmen
+umherzieht, fragst Du eines Tages Robo.
+
+**Du**: Sag mal, hast du dir je Gedanken dazu gemacht, wie du eigentlich funktionierts?
+
+**Robo**: Was meinst du, wie ich funktioniere? Ich bin halt… ich…
+
+**Du**: Ja schon, aber was woher weisst du denn alles was du weisst?
+
+**Robo**: Das kann ich dir sagen. Früher habe ich viele Datenträger verschlungen,
+und dadurch gelernt.
+
+**Du**: Ob so eine Diskette wohl lecker schmeckt? Egal, ich hab ein paar Fragen zu deinem
+Lean-Modul.
+
+**Robo**: Na dann nur zu!"
diff --git a/server/adam/Adam/Levels/Lean/L01_Type.lean b/server/adam/Adam/Levels/Lean/L01_Type.lean
new file mode 100644
index 0000000..eb4a62d
--- /dev/null
+++ b/server/adam/Adam/Levels/Lean/L01_Type.lean
@@ -0,0 +1,41 @@
+import Adam.Metadata
+
+import Mathlib
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Lean"
+Level 1
+
+Title "Typen"
+
+Introduction
+"
+**Du**: Also, wieso schreib ich denn sowohl `(n : ℕ)` für eine natürliche Zahl wie
+auch `(h : A ∧ ¬ B)` für eine Aussage?
+
+**Robo**: Alles in Lean sind Objekte von einem *Typen*, man nennt das auch
+\"dependent type theory\". Rechts vom `:` steht immer der Typ der dieses Objekt hat.
+
+**Du**: Verstehe, dann war `ℕ` der Typ der natürlichen Zahlen, `Prop` der Typ
+aller logischen Aussagen, und so weiter. Un wenn `R` einfach irgendein Typ ist, dann…
+
+**Robot: …würdest du das als `(R : Type)` schreiben.
+
+**Du**: Also sind Typen ein bisschen jene Grundlage, die in meinem Studium die
+Mengen eingenommen haben?
+
+**Robo**: Genau. Ein Ring ist dann zum Beispiel als `(R : Type) [Ring R]` definiert,
+also als Typen, auf dem eine Ringstruktur besteht.
+
+**Robo**: Hier ein Beispiel. Die Taktik `ring` funktioniert in jedem Typen, der
+genügend Struktur definiert hat, zum Beispiel in einem kommutativen Ring:
+"
+
+Statement (R : Type) [CommRing R] (a b : R) : a + b = b + a := by
+  ring
+
+Conclusion "**Robo**: `[CommRing R]` nennt man übrigens eine Instanz und die
+eckigen Klammern sagen Lean, dass es automatisch suchen soll, ob es so eine Instanz
+findet, wenn man ein Lemma anwenden will."
diff --git a/server/adam/Adam/Levels/Lean/L02_Universe.lean b/server/adam/Adam/Levels/Lean/L02_Universe.lean
new file mode 100644
index 0000000..c20c171
--- /dev/null
+++ b/server/adam/Adam/Levels/Lean/L02_Universe.lean
@@ -0,0 +1,44 @@
+import Adam.Metadata
+
+import Mathlib
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Lean"
+Level 2
+
+Title "Universen"
+
+Introduction
+"**Du**: Aber wenn alles Typen sind, welcher Typ hat dann `Type`?
+
+**Robo**: `Type 1` und dieser hat Typ `Type 2`, etc.
+
+**Robo**: Die Zahl nennt man *Universum*. Manchmal führt man Universen explizit
+mit `universum u` ein, öfter siehst du `(R : Type _)`, was einfach ein Platzhalter
+für irgend ein Universum ist.
+
+**Du**: Das klingt ein bisschen nach Mengentheoretische Probleme, die man normalerweise
+ignoriert.
+
+**Robo**: Genau! Deshalb schreibt man eigentlich immer einfach `Type _` und ist glücklich.
+Spezifischer muss man erst werden wenn man sowas wie Kategorientheorie anschaut, wo
+man die Universen tatsächlich kontrollieren muss.
+
+**Du**: Oke, hier rein, da raus. Aber hast du mir noch eine Aufgabe?
+"
+
+universe u
+
+Statement
+    (R : Type u) [CommRing R] (a b : R) : a + b = b + a := by
+  Hint "**Robo**: Naja, Aufgaben zu Universen sind nicht so natürlich,
+  aber vorige Aufgabe würde man eigentlich besser so schreiben, da
+  kannst du mindestens das Uniersum beobachten."
+  ring
+
+Conclusion "**Du**: Na dann. Aber gut dass ich's mal gesehen hab."
+
+-- Hint (R : Type) (h : CommRing R) (a : R) (b : R) : a + b = b + a =>
+-- ""
diff --git a/server/adam/Adam/Levels/Lean/L03_ImplicitArguments.lean b/server/adam/Adam/Levels/Lean/L03_ImplicitArguments.lean
new file mode 100644
index 0000000..19a8411
--- /dev/null
+++ b/server/adam/Adam/Levels/Lean/L03_ImplicitArguments.lean
@@ -0,0 +1,71 @@
+import Adam.Metadata
+
+import Mathlib
+import Adam.ToBePorted
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Lean"
+Level 3
+
+Title "Implizite Argumente"
+
+Introduction
+"
+**Du**: Was mich aber mehr beschäftigt, ist, dass Lemmas manchmal viel mehr Argumente
+haben als ich hinschreiben muss.
+
+**Robo**: Lean kann manche Argumente aus dem Kontext erschliessen. Hast du zum Beispiel
+ein Lemma von vorhin
+
+```
+lemma Fin.sum_univ_castSucc {β : Type _} [AddCommMonoid β] {n : ℕ} (f : Fin (n + 1) → β) :
+    ∑ i : Fin (n + 1), f i = ∑ i : Fin n, f (↑Fin.castSucc.toEmbedding i) + f (Fin.last n) := by
+  sorry
+```
+
+dann reicht es ja Lean `f` zu geben und daraus kann es herausfinden, was die anderen
+(`β`, `n`) sein müssen.
+
+**Robo**: Solche *implizite Argumente* markiert man dann mit `{_ : _}` während
+*explizite Arumente* mit `(_ : _)` markiert werden.
+
+**Du**: Dann könnte ich also einfach `Fin.sum_univ_castSucc f` schreiben?
+
+**Robo**: Genau!
+
+**Du**: Und was war dann das `(n := m + 1)` vorhin genau?
+
+**Robo**: Damit kann man im Aussnahmefall die impliziten Argumente doch angeben. Hier haben wir
+gesagt, es soll für das Argument `n` den Term `m + 1` einsetzen. Hier mach das doch noch einmal
+unter weniger Stress:
+"
+
+open BigOperators
+
+Statement (m : ℕ) : ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i := by
+  Branch
+    rw [Fin.sum_univ_castSucc]
+    Hint "**Robo**: Siehst du, ohne die Hilfe macht es das Falsche. Deshalb muss man hier
+    explizit mit `Fin.sum_univ_castSucc (n := m + 1)` nachhelfen."
+    rw [Fin.sum_univ_castSucc]
+    Hint "**Robo**: Na klar, in dem Beispiel kannst du einfach weiter umschreiben bis es
+    nicht mehr geht, aber das war nicht der Punkt…"
+    rw [Fin.sum_univ_castSucc]
+    Hint "**Robo**: Na klar, in dem Beispiel kannst du einfach weiter umschreiben bis es
+    nicht mehr geht, aber das war nicht der Punkt…"
+    rfl
+  rw [Fin.sum_univ_castSucc (n := m + 1)]
+  rfl
+
+OnlyTactic rw rfl
+
+Conclusion "**Du**: Gibt es auch noch ander Methoden implizite Argumente anzugeben.
+
+**Robo** `@Fin.sum_univ_castSucc` würde *alle* Argumente explizit machen,
+aber das ist unparktischer, weil man dann irgendwie
+`@Fin.sum_univ_castSucc _ _ (m + 1)` schreiben müsste.
+
+**Du**: Ah und ich sehe der `_` ist überall in Lean ein Platzhalter, der automatisch
+gefüllt wird."
diff --git a/server/adam/Adam/Levels/Lean/L04_InstanceArguments.lean b/server/adam/Adam/Levels/Lean/L04_InstanceArguments.lean
new file mode 100644
index 0000000..dbb5425
--- /dev/null
+++ b/server/adam/Adam/Levels/Lean/L04_InstanceArguments.lean
@@ -0,0 +1,57 @@
+import Adam.Metadata
+
+import Mathlib
+import Adam.ToBePorted
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Lean"
+Level 4
+
+Title "Instanz-Argumente"
+
+Introduction
+"**Du**: Also nochmals als Zusammenfassung, dann gibt es 3 Arten von Argumenten,
+explizite mit `()`, implizite mit `{}` und Instanzen mit `[]`?
+
+**Robo**: Korrekt. Instanzen sind damit auch Implizite Argumente. Der Unterschied
+zwischen `{}` und `[]` ist also *wie* Lean diese füllt.
+
+**Du**: Verstehe, bei den ersten sucht es logisch nach einer richtigen Möglichkeit,
+beim zweiten geht's durch alle Instanzen, die es kennt.
+
+
+**Robo**: Funktioniert hier bei mir nicht, aber wenn du ausserhalb eines Beweises
+`#synth Ring ℤ` in ein Dokument schreibt, zeigt dir Lean, ob es eine Instanz finden kann.
+
+**Du**: Ich glaube das macht alles Sinn.
+
+**Robo**: Hier, mach nochmals das Gleiche wie vorhin aber mit @-Syntax um das zu
+verinnerlichen:
+"
+
+open BigOperators
+
+Statement (m : ℕ) :
+      ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i := by
+  Hint "*Robo*: Schreibe `rw [@Fin.sum_univ_castSucc _ _ (m + 1)]`
+  anstatt `rw [Fin.sum_univ_castSucc (n := m + 1)]`!"
+  rw [@Fin.sum_univ_castSucc _ _ (m + 1)]
+  rfl
+
+OnlyTactic rw rfl
+
+Conclusion "
+**Du**: Danke Robo!
+
+Um zwei weitere Ecken und plötzlich steht ihr wieder vor dem Golem, dem ihr schon begegnet seit.
+Dieser lädt euch zum Abendmahl ein. Ihr erfährt, dass er ganz gerne liest und er zeigt euch
+sein neustes Buch, das er leider nicht lesen kann. Nich tnur ist es der zweite Band einer Serie
+(der Erste hat offensichtlich was mit \"Urbildern\" zu tun), sondern ist es auch in einem
+Dialekt geschrieben, der anscheinend nur auf einem Nachbarsmond gesprochen wird.
+
+Ihr beschliesst dem herzlichen Golem zu helfen und beiden Monden einen Besuch abzustatten,
+sowohl um den Dialekt zu lernen, wie auch in der Bibliothek auf dem anderen Mond nach dem
+ersten Band zu suchen.
+"
diff --git a/server/testgame/TestGame/Levels/LeftOvers/L09_Or.lean b/server/adam/Adam/Levels/LeftOvers/L09_Or.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/LeftOvers/L09_Or.lean
rename to server/adam/Adam/Levels/LeftOvers/L09_Or.lean
index 24297d5..b572c8a 100644
--- a/server/testgame/TestGame/Levels/LeftOvers/L09_Or.lean
+++ b/server/adam/Adam/Levels/LeftOvers/L09_Or.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Implication"
 Level 9
 
diff --git a/server/testgame/TestGame/Levels/LeftOvers/L33_Prime.lean b/server/adam/Adam/Levels/LeftOvers/L33_Prime.lean
similarity index 80%
rename from server/testgame/TestGame/Levels/LeftOvers/L33_Prime.lean
rename to server/adam/Adam/Levels/LeftOvers/L33_Prime.lean
index 1b8393f..419f94a 100644
--- a/server/testgame/TestGame/Levels/LeftOvers/L33_Prime.lean
+++ b/server/adam/Adam/Levels/LeftOvers/L33_Prime.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "Nat2"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/LeftOvers/L34_ExistsUnique.lean b/server/adam/Adam/Levels/LeftOvers/L34_ExistsUnique.lean
similarity index 83%
rename from server/testgame/TestGame/Levels/LeftOvers/L34_ExistsUnique.lean
rename to server/adam/Adam/Levels/LeftOvers/L34_ExistsUnique.lean
index 9abc351..49188d0 100644
--- a/server/testgame/TestGame/Levels/LeftOvers/L34_ExistsUnique.lean
+++ b/server/adam/Adam/Levels/LeftOvers/L34_ExistsUnique.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "Nat2"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/LeftOvers/Lxx_Prime.lean b/server/adam/Adam/Levels/LeftOvers/Lxx_Prime.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/LeftOvers/Lxx_Prime.lean
rename to server/adam/Adam/Levels/LeftOvers/Lxx_Prime.lean
index be43277..f1847f8 100644
--- a/server/testgame/TestGame/Levels/LeftOvers/Lxx_Prime.lean
+++ b/server/adam/Adam/Levels/LeftOvers/Lxx_Prime.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
@@ -21,7 +21,7 @@ lemma even_square (n : ℕ) : even n → even (n ^ 2) := by
 
 def prime (n : ℕ) : Prop := (2 ≤ n) ∧ ∀ a b, n = a * b → a = 1 ∨ b = 1
 
-Game "TestGame"
+Game "Adam"
 World "Nat"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/LeftOvers/Lxx_Tauto.lean b/server/adam/Adam/Levels/LeftOvers/Lxx_Tauto.lean
similarity index 100%
rename from server/testgame/TestGame/Levels/LeftOvers/Lxx_Tauto.lean
rename to server/adam/Adam/Levels/LeftOvers/Lxx_Tauto.lean
diff --git a/server/testgame/TestGame/Levels/LeftOvers/Lxx_Tfae.lean b/server/adam/Adam/Levels/LeftOvers/Lxx_Tfae.lean
similarity index 100%
rename from server/testgame/TestGame/Levels/LeftOvers/Lxx_Tfae.lean
rename to server/adam/Adam/Levels/LeftOvers/Lxx_Tfae.lean
diff --git a/server/testgame/TestGame/Levels/LeftOvers/Playground.lean b/server/adam/Adam/Levels/LeftOvers/Playground.lean
similarity index 92%
rename from server/testgame/TestGame/Levels/LeftOvers/Playground.lean
rename to server/adam/Adam/Levels/LeftOvers/Playground.lean
index 7622e0b..b1f5e6a 100644
--- a/server/testgame/TestGame/Levels/LeftOvers/Playground.lean
+++ b/server/adam/Adam/Levels/LeftOvers/Playground.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
 -- -- INCORPORATED
diff --git a/server/testgame/TestGame/Levels/LeftOvers/xx_Functions.lean b/server/adam/Adam/Levels/LeftOvers/xx_Functions.lean
similarity index 91%
rename from server/testgame/TestGame/Levels/LeftOvers/xx_Functions.lean
rename to server/adam/Adam/Levels/LeftOvers/xx_Functions.lean
index 061d9a7..87d457f 100644
--- a/server/testgame/TestGame/Levels/LeftOvers/xx_Functions.lean
+++ b/server/adam/Adam/Levels/LeftOvers/xx_Functions.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "Function"
 Level 1
 
diff --git a/server/adam/Adam/Levels/LinearAlgebra.lean b/server/adam/Adam/Levels/LinearAlgebra.lean
new file mode 100644
index 0000000..0bb386d
--- /dev/null
+++ b/server/adam/Adam/Levels/LinearAlgebra.lean
@@ -0,0 +1,41 @@
+import Adam.Levels.LinearAlgebra.L01_Module
+import Adam.Levels.LinearAlgebra.L02_VectorNotation
+import Adam.Levels.LinearAlgebra.L03_VectorNotation
+import Adam.Levels.LinearAlgebra.L04_Submodule
+import Adam.Levels.LinearAlgebra.L05_Submodule
+import Adam.Levels.LinearAlgebra.L06_Span
+import Adam.Levels.LinearAlgebra.L07_Span
+import Adam.Levels.LinearAlgebra.L08_GeneratingSet
+
+import Adam.Levels.LinearAlgebra.M01_LinearMap
+import Adam.Levels.LinearAlgebra.M02_LinearIndep
+import Adam.Levels.LinearAlgebra.M04_Basis
+
+import Adam.Levels.LinearAlgebra.N01_Span
+import Adam.Levels.LinearAlgebra.N02_Span
+import Adam.Levels.LinearAlgebra.N03_Idempotent
+import Adam.Levels.LinearAlgebra.N04_Idempotent
+import Adam.Levels.LinearAlgebra.N05_Sum
+import Adam.Levels.LinearAlgebra.N06_Sum
+import Adam.Levels.LinearAlgebra.N07_Prod
+import Adam.Levels.LinearAlgebra.N08_Prod
+import Adam.Levels.LinearAlgebra.N09_Prod
+
+Game "Adam"
+World "Module"
+Title "Vektorraum"
+
+Introduction "Hier lernst du die Grundlagen zur linearen Algebra.
+
+Vektorräume sind in Lean etwas algemeiner definiert als dies normalerweise in
+einer Einführungsvorlesung antrifft: Man definiert ein \"Modul\" (Plural: Moduln)
+über einem Ring. Ein Modul über einem *Körper* wird dann auch \"Vektorraum\" genannt.
+"
+
+Game "Adam"
+World "Basis"
+Title "Lineare Abbildungen"
+
+Game "Adam"
+World "Module2"
+Title "Mehr Vektorräume"
diff --git a/server/adam/Adam/Levels/LinearAlgebra/L01_Module.lean b/server/adam/Adam/Levels/LinearAlgebra/L01_Module.lean
new file mode 100644
index 0000000..d1866ec
--- /dev/null
+++ b/server/adam/Adam/Levels/LinearAlgebra/L01_Module.lean
@@ -0,0 +1,106 @@
+import Adam.Metadata
+
+import Mathlib.Data.Real.Basic      -- definiert `ℝ`
+import Mathlib.Algebra.Module.Basic -- definiert `module`
+import Mathlib.Tactic.LibrarySearch
+import Adam.StructInstWithHoles
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Module"
+Level 1
+
+Title "Module"
+
+Introduction
+"
+Konkret heisst das:
+
+Sei `R` ein Ring. Ein `R`-Modul ist eine kommutative Gruppe `(V, +)` zusammen mit
+einer Abbildung `• : R × V → V` (Skalarmultiplitation genannt), die folgende
+Eigenschaften beliebige `(r s : R)` und `(v w : V)`erfüllt:
+- `r • (v + w) = r • v + r • w`
+- `(r + s) • v = r • v + s • v`
+- `(r * s) • v = r • s • v`
+- `1 • r = r`
+- `0 • v = 0`
+- `r • 0 = 0`
+
+"
+
+-- Bemerkungen:
+-- 1) Über einem `[field R]` sind die letzten beiden Eigenschaften überflüssig, diese kann
+--    man beweisen, wenn man Cancellation (`a₁ + x = a₂ + x → a₁ = a₂`) hat. In einem generellen
+--    Ring, muss das aber nicht gegeben sein (siehe Nullteiler).
+-- 2) Die nötigen Annahmen um ein Modul in Lean zu erhalten sind tatsächlich noch etwas lockerer,
+--    so muss `R` nicht ganz ein Ring sein (nur `[Semiring R]`) und
+--    `V` muss nicht ganz eine kommutative Gruppe sein (nur `[add_comm_monoid V]`).
+-- Einen abstrakten Vektorraum definiert man wie folgt:
+-- `variables {R V : Type*} [field R] [add_comm_monoid V] [module R V]`
+
+-- Wenn man hingegen konkret zeigen will, dass ein existierendes Objekt ein Vektorraum ist,
+-- kann man eine einsprechende Instanz wie folgt definieren:
+
+-- ```
+-- instance Q_module : Module ℚ ℝ :=
+-- { smul := λa r, ↑a * r
+--   smul_zero := _
+--   zero_smul := _
+--   one_smul := _
+--   smul_add := _
+--   add_smul := _
+--   mul_smul := _ }
+-- ```
+-- Man muss also angeben, welche Skalarmultiplikation man gerne hätte
+-- (`smul`. In unserem Fall sagen wir einfach, diese soll Multiplikation in `ℝ` sein.)
+-- und dazu jegliche Beweise, dass die Skalarmultiplikation sich mit der Ringstruktur verträgt.
+-- Im nachfolgenden beweisen wir die Eigenschaften einzeln.
+
+Statement
+"Zeige, dass $\\mathbb{R}$ ein $\\mathbb{Q}$-Modul ist."
+    : Module ℚ ℝ := by
+  Hint "**Robo**: Als erstes willst du die Stuktur `Modul` aufteilen in einzelne Beweise.
+  Der Syntax dafür ist:
+
+  ```
+  refine \{ ?..! }
+  ```
+  "
+  refine { ?..! }
+  · Hint "**Robo**: Hier musst du die Skalarmultiplikation angeben.
+    Benutze dafür `exact fun (a : ℚ) (r : ℝ) => ↑a * r`."
+    exact fun (a : ℚ) (r : ℝ) => ↑a * r
+  · Hint "**Robo**: Jetzt musst du alle eigenschaften eines $\\mathbb\{Q}$-Moduls zeigen,
+    das sind also 6 einzelne Goals."
+    intro b
+    Hint "**Robo**: Mit `change (1 : ℚ) * {b} = {b}` kannst du das Goal umschreiben, damit
+    dann andere Taktiken besser damit arbeiten können."
+    change (1 : ℚ) * b = b
+    Hint "**Robo**: Den Teil kannst du mit `simp` beweisen."
+    simp
+  · intro x y b
+    Hint "**Robo**: Benutze `change` um `•` durch `*` zu ersetzen."
+    Hint (hidden := true) "**Robo**: Explizit `change ({x} * {y} : ℚ) * {b} = {x} * ({y} * {b})`"
+    change (x * y : ℚ) * b = x * (y * b)
+    Hint "**Robo**: Mit `simp` und `ring` kannst du den Rest beweisen."
+    simp
+    ring
+  · intro a
+    simp
+  · intro a x y
+    Hint (hidden := true) "**Robo**: Explizit `change {a} * ({x} + {y}) = {a} * {x} + {a} * {y}`"
+    change a * (x + y) = a * x + a * y
+    ring
+  · intro r s x
+    Hint (hidden := true) "**Robo**: Explizit
+    `change ({r} + {s} : ℚ) * {x} = {r} * {x} + {s} * {x}`"
+    change (r + s : ℚ) * x = r * x + s * x
+    simp
+    ring
+  · intro a
+    Hint (hidden := true) "**Robo**: Explizit `change (0 : ℚ) * {a} = 0`"
+    change (0 : ℚ) * a = 0
+    simp
+
+NewTactic refine exact change
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L02_VectorNotation.lean b/server/adam/Adam/Levels/LinearAlgebra/L02_VectorNotation.lean
similarity index 55%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L02_VectorNotation.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L02_VectorNotation.lean
index 0e77ca7..c0b6be3 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L02_VectorNotation.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L02_VectorNotation.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
 import Mathlib.Algebra.Module.Pi          -- definiert `Module ℚ (fin 2 → ℚ)`
@@ -7,7 +7,7 @@ import Mathlib.Tactic.FinCases
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 2
 
@@ -15,30 +15,14 @@ Title "Konkrete Vektorräume"
 
 Introduction
 "
-Häufig in der linearen Algebra hat man ganz einfach Vektoren über `ℚ` oder `ℝ`
-und möchte diese explizit definieren.
-
-Reele Vektorräume definiert man in Lean am besten als Funktion von einem Indexset.
-
-So ist `Fin 2` eine Menge, die nur `0` und `1` enthält
-und `ℚ²` wird als `Fin 2 → ℚ` definiert. Hier machen wir uns eine
-lokale notation dafür:
+Den $\\mathbb{Q}$-Vektorraum $\\mathbb{Q}^3$ definiert man am besten mit
+der lokalen Notation
 
 ```
-notation `ℚ²` := Fin 2 → ℚ
+local notation `ℚ³` := Fin 3 → ℚ
 ```
 
-Das mag auf den ersten Blick etwas unintuitiv erscheinen, hat aber den Vorteil,
-dass man die ganze
-Infrastruktur für Funktionen einfach direkt für Vektoren und
-Matrizen mitgebrauchen kann.
-
-Wir können uns auch noch ein paar andere standardmässige `ℚ`-Vektorräume definieren.
-
-```
-notation \"ℚ³\" => Fin 3 → ℚ
-notation \"ℚ^(\" n \")\" => (Fin n) → ℚ
-```
+Dabei ist `Fin 3` die Indexmenge $\\{0, 1, 2\\}$.
 
 Die schreibweise für einen Vektor ist `![ _, _ ]`. Zu beachten ist,
 dass man bei Zahlen explizit einen Typ angeben muss, sonst denkt sich
@@ -61,8 +45,8 @@ Dann eine Vektorgleichung komponentenweise aufteilt.
 Für jede Komponente kann man dann mit `simp` und `ring` weiterkommen.
 "
 
-notation "ℚ³" => Fin 3 → ℚ
-notation "ℚ^(" n ")" => (Fin n) → ℚ
+local notation "ℚ³" => Fin 3 → ℚ
+local notation "ℚ^(" n ")" => (Fin n) → ℚ
 
 Statement
 ""
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L03_VectorNotation.lean b/server/adam/Adam/Levels/LinearAlgebra/L03_VectorNotation.lean
similarity index 92%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L03_VectorNotation.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L03_VectorNotation.lean
index 839bd94..b49b982 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L03_VectorNotation.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L03_VectorNotation.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
 import Mathlib.Algebra.Module.Pi          -- definiert `Module ℚ (fin 2 → ℚ)`
 import Mathlib.Data.Fin.VecNotation
 import Mathlib.Tactic.FinCases
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L04_Submodule.lean b/server/adam/Adam/Levels/LinearAlgebra/L04_Submodule.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L04_Submodule.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L04_Submodule.lean
index 42667d3..964e47a 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L04_Submodule.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L04_Submodule.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L05_Submodule.lean b/server/adam/Adam/Levels/LinearAlgebra/L05_Submodule.lean
similarity index 92%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L05_Submodule.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L05_Submodule.lean
index 860a2aa..6709165 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L05_Submodule.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L05_Submodule.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L06_Span.lean b/server/adam/Adam/Levels/LinearAlgebra/L06_Span.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L06_Span.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L06_Span.lean
index ae9b8ab..8d309d0 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L06_Span.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L06_Span.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
@@ -8,7 +8,7 @@ import Mathlib.Tactic.FinCases
 import Mathlib.Algebra.BigOperators.Finsupp -- default?
 import Mathlib.LinearAlgebra.Span
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 6
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L07_Span.lean b/server/adam/Adam/Levels/LinearAlgebra/L07_Span.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L07_Span.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L07_Span.lean
index f047823..a50946b 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L07_Span.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L07_Span.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
@@ -10,7 +10,7 @@ import Mathlib.LinearAlgebra.Span
 import Mathlib.Tactic.LibrarySearch
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 7
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L08_GeneratingSet.lean b/server/adam/Adam/Levels/LinearAlgebra/L08_GeneratingSet.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/LinearAlgebra/L08_GeneratingSet.lean
rename to server/adam/Adam/Levels/LinearAlgebra/L08_GeneratingSet.lean
index 32bc7bd..9d20601 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L08_GeneratingSet.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/L08_GeneratingSet.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
@@ -8,7 +8,7 @@ import Mathlib.Tactic.FinCases
 import Mathlib.Algebra.BigOperators.Finsupp -- default?
 import Mathlib.LinearAlgebra.Span
 
-Game "TestGame"
+Game "Adam"
 World "Module"
 Level 8
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/M01_LinearMap.lean b/server/adam/Adam/Levels/LinearAlgebra/M01_LinearMap.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/LinearAlgebra/M01_LinearMap.lean
rename to server/adam/Adam/Levels/LinearAlgebra/M01_LinearMap.lean
index bf6d590..258e0d4 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/M01_LinearMap.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/M01_LinearMap.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Real.Basic           -- definiert `ℝ`
 import Mathlib.Algebra.Module.LinearMap -- definiert `→ₗ`
 import Mathlib.Tactic.FinCases
 import Mathlib.Data.Fin.VecNotation
 
-Game "TestGame"
+Game "Adam"
 World "Basis"
 Level 1
 
diff --git a/server/adam/Adam/Levels/LinearAlgebra/M02_LinearIndep.lean b/server/adam/Adam/Levels/LinearAlgebra/M02_LinearIndep.lean
new file mode 100644
index 0000000..359fe45
--- /dev/null
+++ b/server/adam/Adam/Levels/LinearAlgebra/M02_LinearIndep.lean
@@ -0,0 +1,49 @@
+import Adam.Metadata
+
+import Mathlib.Algebra.Module.Submodule.Lattice
+import Mathlib.Data.Real.Basic           -- definiert `ℝ`
+import Mathlib.Algebra.Module.LinearMap -- definiert `→ₗ`
+import Mathlib.Tactic.FinCases
+import Mathlib.Data.Fin.VecNotation
+-- import Mathlib.LinearAlgebra.Finsupp
+import Mathlib.Algebra.BigOperators.Basic -- default
+-- import Mathlib.LinearAlgebra.LinearIndependent
+import Mathlib
+
+Game "Adam"
+World "Basis"
+Level 2
+
+Title "Lineare Unabhängigkeit"
+
+namespace Ex_LinIndep
+
+scoped notation "ℝ²" => Fin 2 → ℝ
+
+Introduction
+"
+"
+
+Statement
+"Zeige, dass `![1, 0], ![1, 1]` linear unabhängig über `ℝ` sind."
+    : LinearIndependent ℝ ![(![1, 0] : ℝ²), ![1, 1]] := by
+  Hint "`rw [Fintype.linearIndependent_iff]`"
+  rw [Fintype.linearIndependent_iff]
+  Hint "`intros c h`"
+  intros c h
+  Hint "BUG: `simp at h` does not work :("
+  simp at h -- doesn't work
+  sorry
+
+  -- rw [Fintype.linearIndependent_iff]
+  -- intros c h
+  -- simp at h
+  -- intros i
+  -- fin_cases i
+  -- swap
+  -- { exact h.2 }
+  -- { have h' := h.1
+  --   rw [h.2, add_zero] at h'
+  --   exact h'}
+
+end Ex_LinIndep
diff --git a/server/adam/Adam/Levels/LinearAlgebra/M04_Basis.lean b/server/adam/Adam/Levels/LinearAlgebra/M04_Basis.lean
new file mode 100644
index 0000000..c8145e1
--- /dev/null
+++ b/server/adam/Adam/Levels/LinearAlgebra/M04_Basis.lean
@@ -0,0 +1,32 @@
+import Adam.Metadata
+
+import Mathlib.Algebra.Module.Submodule.Lattice
+import Mathlib
+
+Game "Adam"
+World "Basis"
+Level 4
+
+Title "Basis"
+
+namespace Ex_Basis
+
+scoped notation "ℝ²" => Fin 2 → ℝ
+
+open Submodule
+
+Introduction
+"
+
+"
+
+lemma exercise1 : LinearIndependent ℝ ![(![1, 0] : ℝ²), ![1, 1]] := sorry
+
+lemma exercise2 :  ⊤ ≤ span ℝ (Set.range ![(![1, 0] : Fin 2 → ℝ), ![1, 1]]) := sorry
+
+Statement : Basis (Fin 2) ℝ ℝ² := by
+  apply Basis.mk
+  apply exercise1
+  apply exercise2
+
+end Ex_Basis
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N01_Span.lean b/server/adam/Adam/Levels/LinearAlgebra/N01_Span.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N01_Span.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N01_Span.lean
index b8d587a..c9d4aaf 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N01_Span.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N01_Span.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
@@ -8,7 +8,7 @@ import Mathlib.Tactic.FinCases
 import Mathlib.Algebra.BigOperators.Finsupp -- default?
 import Mathlib.LinearAlgebra.Span
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N02_Span.lean b/server/adam/Adam/Levels/LinearAlgebra/N02_Span.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N02_Span.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N02_Span.lean
index 8d2e82c..decc953 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N02_Span.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N02_Span.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic            -- definiert `ℝ`
@@ -11,7 +11,7 @@ import Mathlib
 
 open Submodule
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N03_Idempotent.lean b/server/adam/Adam/Levels/LinearAlgebra/N03_Idempotent.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N03_Idempotent.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N03_Idempotent.lean
index 02cf3b4..ceb7558 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N03_Idempotent.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N03_Idempotent.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic
 import Mathlib.LinearAlgebra.Basic
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N04_Idempotent.lean b/server/adam/Adam/Levels/LinearAlgebra/N04_Idempotent.lean
similarity index 93%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N04_Idempotent.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N04_Idempotent.lean
index 26a956d..fecaebb 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N04_Idempotent.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N04_Idempotent.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic
 import Mathlib.LinearAlgebra.Basic
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N05_Sum.lean b/server/adam/Adam/Levels/LinearAlgebra/N05_Sum.lean
similarity index 92%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N05_Sum.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N05_Sum.lean
index 0490708..18ad88c 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N05_Sum.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N05_Sum.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.LinearAlgebra.Span
 
 open Submodule
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N06_Sum.lean b/server/adam/Adam/Levels/LinearAlgebra/N06_Sum.lean
similarity index 92%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N06_Sum.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N06_Sum.lean
index a4655c3..d571449 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N06_Sum.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N06_Sum.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.LinearAlgebra.Span
 
 open Submodule
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 6
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N07_Prod.lean b/server/adam/Adam/Levels/LinearAlgebra/N07_Prod.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N07_Prod.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N07_Prod.lean
index 606d3c5..ff1f973 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N07_Prod.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N07_Prod.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic
 import Mathlib.LinearAlgebra.Span
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 7
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N08_Prod.lean b/server/adam/Adam/Levels/LinearAlgebra/N08_Prod.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N08_Prod.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N08_Prod.lean
index 853c9dd..3dcc9a0 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N08_Prod.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N08_Prod.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic
@@ -6,7 +6,7 @@ import Mathlib.LinearAlgebra.Span
 
 universe u
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 8
 
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/N09_Prod.lean b/server/adam/Adam/Levels/LinearAlgebra/N09_Prod.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/LinearAlgebra/N09_Prod.lean
rename to server/adam/Adam/Levels/LinearAlgebra/N09_Prod.lean
index 0764a87..5b08aa3 100644
--- a/server/testgame/TestGame/Levels/LinearAlgebra/N09_Prod.lean
+++ b/server/adam/Adam/Levels/LinearAlgebra/N09_Prod.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Algebra.Module.Submodule.Lattice
 import Mathlib.Data.Real.Basic
 import Mathlib.LinearAlgebra.Span
 
-Game "TestGame"
+Game "Adam"
 World "Module2"
 Level 9
 
diff --git a/server/testgame/TestGame/Levels/Notes.txt b/server/adam/Adam/Levels/Notes.txt
similarity index 100%
rename from server/testgame/TestGame/Levels/Notes.txt
rename to server/adam/Adam/Levels/Notes.txt
diff --git a/server/adam/Adam/Levels/Numbers.lean b/server/adam/Adam/Levels/Numbers.lean
new file mode 100644
index 0000000..6a6f2fa
--- /dev/null
+++ b/server/adam/Adam/Levels/Numbers.lean
@@ -0,0 +1,2 @@
+import Adam.Levels.Numbers.L01_PNat
+import Adam.Levels.Numbers.L02_PNat
diff --git a/server/testgame/TestGame/Levels/Numbers/L01_PNat.lean b/server/adam/Adam/Levels/Numbers/L01_PNat.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Numbers/L01_PNat.lean
rename to server/adam/Adam/Levels/Numbers/L01_PNat.lean
index fa1a217..d45f07a 100644
--- a/server/testgame/TestGame/Levels/Numbers/L01_PNat.lean
+++ b/server/adam/Adam/Levels/Numbers/L01_PNat.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Numbers"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/Numbers/L02_PNat.lean b/server/adam/Adam/Levels/Numbers/L02_PNat.lean
similarity index 89%
rename from server/testgame/TestGame/Levels/Numbers/L02_PNat.lean
rename to server/adam/Adam/Levels/Numbers/L02_PNat.lean
index bca2e8f..b073a3c 100644
--- a/server/testgame/TestGame/Levels/Numbers/L02_PNat.lean
+++ b/server/adam/Adam/Levels/Numbers/L02_PNat.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Numbers"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/Predicate.lean b/server/adam/Adam/Levels/Predicate.lean
similarity index 65%
rename from server/testgame/TestGame/Levels/Predicate.lean
rename to server/adam/Adam/Levels/Predicate.lean
index d5c4135..de8b91a 100644
--- a/server/testgame/TestGame/Levels/Predicate.lean
+++ b/server/adam/Adam/Levels/Predicate.lean
@@ -1,14 +1,14 @@
-import TestGame.Levels.Predicate.L01_Ring
-import TestGame.Levels.Predicate.L02_Rewrite
-import TestGame.Levels.Predicate.L03_Rewrite
-import TestGame.Levels.Predicate.L04_Ring
-import TestGame.Levels.Predicate.L05_Rfl
-import TestGame.Levels.Predicate.L06_Exists
-import TestGame.Levels.Predicate.L07_Exists
-import TestGame.Levels.Predicate.L08_Forall
-import TestGame.Levels.Predicate.L09_PushNeg
+import Adam.Levels.Predicate.L01_Ring
+import Adam.Levels.Predicate.L02_Rewrite
+import Adam.Levels.Predicate.L03_Rewrite
+import Adam.Levels.Predicate.L04_Ring
+import Adam.Levels.Predicate.L05_Rfl
+import Adam.Levels.Predicate.L06_Exists
+import Adam.Levels.Predicate.L07_Exists
+import Adam.Levels.Predicate.L08_Forall
+import Adam.Levels.Predicate.L09_PushNeg
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Title "Prädikate"
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L01_Ring.lean b/server/adam/Adam/Levels/Predicate/L01_Ring.lean
similarity index 95%
rename from server/testgame/TestGame/Levels/Predicate/L01_Ring.lean
rename to server/adam/Adam/Levels/Predicate/L01_Ring.lean
index ca8b143..fe84bac 100644
--- a/server/testgame/TestGame/Levels/Predicate/L01_Ring.lean
+++ b/server/adam/Adam/Levels/Predicate/L01_Ring.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Ring
 
 --set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L02_Rewrite.lean b/server/adam/Adam/Levels/Predicate/L02_Rewrite.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Predicate/L02_Rewrite.lean
rename to server/adam/Adam/Levels/Predicate/L02_Rewrite.lean
index a45d6cf..0585180 100644
--- a/server/testgame/TestGame/Levels/Predicate/L02_Rewrite.lean
+++ b/server/adam/Adam/Levels/Predicate/L02_Rewrite.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L03_Rewrite.lean b/server/adam/Adam/Levels/Predicate/L03_Rewrite.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Predicate/L03_Rewrite.lean
rename to server/adam/Adam/Levels/Predicate/L03_Rewrite.lean
index be4df47..b841059 100644
--- a/server/testgame/TestGame/Levels/Predicate/L03_Rewrite.lean
+++ b/server/adam/Adam/Levels/Predicate/L03_Rewrite.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L04_Ring.lean b/server/adam/Adam/Levels/Predicate/L04_Ring.lean
similarity index 95%
rename from server/testgame/TestGame/Levels/Predicate/L04_Ring.lean
rename to server/adam/Adam/Levels/Predicate/L04_Ring.lean
index 60291dc..8dd287f 100644
--- a/server/testgame/TestGame/Levels/Predicate/L04_Ring.lean
+++ b/server/adam/Adam/Levels/Predicate/L04_Ring.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L05_Rfl.lean b/server/adam/Adam/Levels/Predicate/L05_Rfl.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Predicate/L05_Rfl.lean
rename to server/adam/Adam/Levels/Predicate/L05_Rfl.lean
index e621f96..39b0ee3 100644
--- a/server/testgame/TestGame/Levels/Predicate/L05_Rfl.lean
+++ b/server/adam/Adam/Levels/Predicate/L05_Rfl.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L06_Exists.lean b/server/adam/Adam/Levels/Predicate/L06_Exists.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/Predicate/L06_Exists.lean
rename to server/adam/Adam/Levels/Predicate/L06_Exists.lean
index 79fd82b..f9d91be 100644
--- a/server/testgame/TestGame/Levels/Predicate/L06_Exists.lean
+++ b/server/adam/Adam/Levels/Predicate/L06_Exists.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
@@ -8,7 +8,7 @@ import Mathlib.Algebra.Parity
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 6
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L07_Exists.lean b/server/adam/Adam/Levels/Predicate/L07_Exists.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Predicate/L07_Exists.lean
rename to server/adam/Adam/Levels/Predicate/L07_Exists.lean
index 26bb955..353b39e 100644
--- a/server/testgame/TestGame/Levels/Predicate/L07_Exists.lean
+++ b/server/adam/Adam/Levels/Predicate/L07_Exists.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
@@ -8,7 +8,7 @@ import Mathlib.Algebra.Parity
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 7
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L08_Forall.lean b/server/adam/Adam/Levels/Predicate/L08_Forall.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Predicate/L08_Forall.lean
rename to server/adam/Adam/Levels/Predicate/L08_Forall.lean
index ff581b2..0e019e4 100644
--- a/server/testgame/TestGame/Levels/Predicate/L08_Forall.lean
+++ b/server/adam/Adam/Levels/Predicate/L08_Forall.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
@@ -7,7 +7,7 @@ import Mathlib.Tactic.Ring
 import Mathlib.Algebra.Parity
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 8
 
diff --git a/server/testgame/TestGame/Levels/Predicate/L09_PushNeg.lean b/server/adam/Adam/Levels/Predicate/L09_PushNeg.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Predicate/L09_PushNeg.lean
rename to server/adam/Adam/Levels/Predicate/L09_PushNeg.lean
index 9eeab66..0c5bc91 100644
--- a/server/testgame/TestGame/Levels/Predicate/L09_PushNeg.lean
+++ b/server/adam/Adam/Levels/Predicate/L09_PushNeg.lean
@@ -1,12 +1,12 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.PushNeg
 import Mathlib
 
 import Mathlib.Algebra.Parity
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Predicate"
 Level 9
 
@@ -106,4 +106,4 @@ ist deine!
 "
 
 NewTactic push_neg
-NewLemma even_iff_not_odd odd_iff_not_even not_exists not_forall
+NewLemma Nat.even_iff_not_odd Nat.odd_iff_not_even not_exists not_forall
diff --git a/server/adam/Adam/Levels/Prime.lean b/server/adam/Adam/Levels/Prime.lean
new file mode 100644
index 0000000..6f1e466
--- /dev/null
+++ b/server/adam/Adam/Levels/Prime.lean
@@ -0,0 +1,11 @@
+import Adam.Levels.Prime.L01_Dvd
+-- import Adam.Levels.Prime.L04_Prime
+-- import Adam.Levels.Prime.L05_Prime
+-- import Adam.Levels.Prime.L06_ExistsUnique
+
+Game "Adam"
+World "Prime"
+Title "Teilbarkeit"
+
+Introduction "Ihr schlendert durch die Befestigung ohne direktes Ziel. Und sprecht mit
+verschiedenen Einwohnern."
diff --git a/server/adam/Adam/Levels/Prime/L01_Dvd.lean b/server/adam/Adam/Levels/Prime/L01_Dvd.lean
new file mode 100644
index 0000000..5e826eb
--- /dev/null
+++ b/server/adam/Adam/Levels/Prime/L01_Dvd.lean
@@ -0,0 +1,49 @@
+import Adam.Metadata
+
+import Mathlib.Tactic.Ring
+import Mathlib
+
+Game "Adam"
+World "Prime"
+Level 1
+
+Title "Teilbarkeit"
+
+Introduction
+"
+Ihr begenet einer Frau, die mit Vorschlaghammer und Schaufel anscheinend an einer Erweiterung
+ihres Hauses baut. Im gespräch erzählt sie euch wie die Dornenwände gezüchtet wurden vor ihrer
+Zeit, und über's Wetter und so.
+
+**Handwerkerin**: (*langer Monolog*) …, und dann gestern habe ich zwei Herren überhört,
+wie sie an folgender Aufgabe gesessen sind, könnt ihr mir das erklären?
+"
+
+-- Die Aussage \"$m$ teilt $n$.\" wird in Lean als `m | n` (`\\|`) geschrieben.
+
+-- **Wichtig:** `∣` (Teilbarkeit) ist ein spezielles Unicode Symbol, das nicht dem
+-- senkrechten Strich auf der Tastatur (`|`) entspricht. Man erhält es mit `\\|`.
+
+-- `m ∣ n` bedeutet `∃ c, n = m * c`, das heisst, man kann damit genau gleich umgehen
+-- wie mit einem `∃`-Quantifier.
+
+Statement dvd_add (n m k : ℕ) (h : m ∣ n) (g : m ∣ k) : m ∣ n + k := by
+  Hint "**Robo**: `n ∣ m` bedeutet \"$n$ teilt $m$\", der senkrechte Strich ist allerdings
+  ein spezieller, den man mit `\\|` schreibt.
+  Definiert ist dieses Symbol als `∃ c, n = m * c`.
+
+  **Du**: Dann kann ich direkt `rcases` und `use` verwenden, wie wenns ein `∃` wäre?
+
+  **Robo**: Genau!"
+  Hint (hidden := true) "**Robo**: Fang doch damit an, mit `rcases _ with ⟨x ,hx⟩`
+  alle Hyptothesen aufzuteilen."
+  rcases h with ⟨x, h⟩
+  rcases g with ⟨y, g⟩
+  Hint (hidden := true) "**Robo**: Jetzt musst du mit `use _` eine Zahl angeben so dass
+  `{n} + {k} = {m} * _` gilt."
+  use x + y
+  Hint (hidden := true) "**Du**: Mit ein bisschen umschreiben kann man sicer `ring` verwenden."
+  rw [h, g]
+  ring
+
+DisabledLemma dvd_add
diff --git a/server/adam/Adam/Levels/Prime/L02_Prime.lean b/server/adam/Adam/Levels/Prime/L02_Prime.lean
new file mode 100644
index 0000000..58231bf
--- /dev/null
+++ b/server/adam/Adam/Levels/Prime/L02_Prime.lean
@@ -0,0 +1,51 @@
+import Adam.Metadata
+import Mathlib.Data.Nat.Prime
+
+import Std.Tactic.RCases
+import Mathlib.Tactic.LeftRight
+import Mathlib.Tactic.Contrapose
+import Mathlib.Tactic.Use
+import Mathlib.Tactic.Ring
+
+-- import Data.Nat.Prime
+
+import Adam.ToBePorted
+
+Game "Adam"
+World "Prime"
+Level 2
+
+Title "Primzahlen"
+
+Introduction
+"
+Als nächstes Begnet ihr einem Lehrer, der nachdenkend an der Sonne sitzt.
+
+**Lehrer**: Sagt mal, mich hat heute einer meiner Schüler was gefragt,
+und ich glaube einfach, der ist in so jungen Jahren bereits schlauer als ich.
+
+Hier etwas Kontext:
+"
+
+Statement (p : ℕ) (h : Nat.Prime p) : ∀ (x : ℕ), (x ∣ p) → x = 1 ∨ x = p := by
+  Hint "**Du**: Die einzigen Teiler einer Primzahl sind `1` und `p`, ist das
+  nicht eine der möglichen Definitionen über `ℕ`?
+
+  **Robo**: Doch, oder zumindest fast.
+  Du kannst du mit `rw` und `Nat.prime_def_lt''` eine der Definitionen für `Nat.Prime` einsetzen
+
+  **Du** Könnte ich nicht einfach `unfold Nat.Prime` sagen um mir das anzuschauen.
+
+  **Robo**: Bloss nicht. Das ist so eine Definition, in die du besser nicht hineinschaust!
+  `Nat.Prime p` ist als `Irreducible p` definiert, was wiederum anhand von Einheiten
+  definiert ist… Da verlieren wir uns in Definition die wir im Moment gar nicht brauchen."
+  rw [Nat.prime_def_lt''] at h
+  rcases h with ⟨_, h₂⟩
+  assumption
+
+NewLemma Nat.prime_def_lt''
+
+Conclusion "**Du**: Ich sehe, meine \"Definition\" hätte auch `1` als Primzahl deklariert. Gut,
+dass wir das überprüft haben.
+
+**Lehrer**: Und jetzt kommen wir zu dem, was mir Kopfschmerzen bereitet."
diff --git a/server/adam/Adam/Levels/Prime/L03_Prime.lean b/server/adam/Adam/Levels/Prime/L03_Prime.lean
new file mode 100644
index 0000000..a437d02
--- /dev/null
+++ b/server/adam/Adam/Levels/Prime/L03_Prime.lean
@@ -0,0 +1,41 @@
+import Adam.Metadata
+import Mathlib.Data.Nat.Prime
+
+import Std.Tactic.RCases
+import Mathlib.Tactic.LeftRight
+import Mathlib.Tactic.Contrapose
+import Mathlib.Tactic.Use
+import Mathlib.Tactic.Ring
+
+import Adam.ToBePorted
+
+Game "Adam"
+World "Prime"
+Level 3
+
+Title "Primzahlen"
+
+Introduction
+"
+Der Lehrer erklärt sein Problem.
+
+**Lehrer**: Und dann fragte der Schüler, wie man denn folgendes herleitet.
+Und dabei ist das weit über seiner Altersstufe!
+"
+
+Statement
+  (p : ℕ) (h₂ : 2 ≤ p): Nat.Prime p ↔ ∀ (a b : ℕ), p ∣ a * b → p ∣ a ∨ p ∣ b := by
+  Hint "**Du**: Naja, mal schauen wie weit man mit `intro` und `constructor` kommt…"
+  constructor
+  intro h a b
+  Hint "**Robo**: Stop! Hier helfe ich dir etwas"
+  apply (Nat.Prime.dvd_mul h).mp
+  intro h
+  rw [Nat.prime_iff]
+  unfold Prime
+  rw [Nat.isUnit_iff, ←and_assoc]
+  constructor
+  constructor
+  linarith
+  linarith
+  assumption
diff --git a/server/testgame/TestGame/Levels/Prime/L06_ExistsUnique.lean b/server/adam/Adam/Levels/Prime/L06_ExistsUnique.lean
similarity index 89%
rename from server/testgame/TestGame/Levels/Prime/L06_ExistsUnique.lean
rename to server/adam/Adam/Levels/Prime/L06_ExistsUnique.lean
index bd8a3dc..3094ea7 100644
--- a/server/testgame/TestGame/Levels/Prime/L06_ExistsUnique.lean
+++ b/server/adam/Adam/Levels/Prime/L06_ExistsUnique.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Data.Nat.Prime
 
 import Std.Tactic.RCases
@@ -7,9 +7,9 @@ import Mathlib.Tactic.Contrapose
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Prime"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/Proposition.lean b/server/adam/Adam/Levels/Proposition.lean
similarity index 66%
rename from server/testgame/TestGame/Levels/Proposition.lean
rename to server/adam/Adam/Levels/Proposition.lean
index bf6ec84..640929b 100644
--- a/server/testgame/TestGame/Levels/Proposition.lean
+++ b/server/adam/Adam/Levels/Proposition.lean
@@ -1,19 +1,19 @@
-import TestGame.Levels.Proposition.L00_Tauto
-import TestGame.Levels.Proposition.L01_Rfl
-import TestGame.Levels.Proposition.L02_Assumption
-import TestGame.Levels.Proposition.L03_Assumption
-import TestGame.Levels.Proposition.L04_True
-import TestGame.Levels.Proposition.L05_Not
-import TestGame.Levels.Proposition.L06_False
-import TestGame.Levels.Proposition.L07_ContraNotEq
-import TestGame.Levels.Proposition.L08_Contra
-import TestGame.Levels.Proposition.L09_And
-import TestGame.Levels.Proposition.L10_And
-import TestGame.Levels.Proposition.L11_Or
-import TestGame.Levels.Proposition.L12_Or
-import TestGame.Levels.Proposition.L13_Summary
+import Adam.Levels.Proposition.L00_Tauto
+import Adam.Levels.Proposition.L01_Rfl
+import Adam.Levels.Proposition.L02_Assumption
+import Adam.Levels.Proposition.L03_Assumption
+import Adam.Levels.Proposition.L04_True
+import Adam.Levels.Proposition.L05_Not
+import Adam.Levels.Proposition.L06_False
+import Adam.Levels.Proposition.L07_ContraNotEq
+import Adam.Levels.Proposition.L08_Contra
+import Adam.Levels.Proposition.L09_And
+import Adam.Levels.Proposition.L10_And
+import Adam.Levels.Proposition.L11_Or
+import Adam.Levels.Proposition.L12_Or
+import Adam.Levels.Proposition.L13_Summary
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Title "Aussagenlogik 1"
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L00_Tauto.lean b/server/adam/Adam/Levels/Proposition/L00_Tauto.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/Proposition/L00_Tauto.lean
rename to server/adam/Adam/Levels/Proposition/L00_Tauto.lean
index 75a5ec7..041a578 100644
--- a/server/testgame/TestGame/Levels/Proposition/L00_Tauto.lean
+++ b/server/adam/Adam/Levels/Proposition/L00_Tauto.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Tactic.Tauto
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L01_Rfl.lean b/server/adam/Adam/Levels/Proposition/L01_Rfl.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Proposition/L01_Rfl.lean
rename to server/adam/Adam/Levels/Proposition/L01_Rfl.lean
index 3c56590..984e7f9 100644
--- a/server/testgame/TestGame/Levels/Proposition/L01_Rfl.lean
+++ b/server/adam/Adam/Levels/Proposition/L01_Rfl.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L02_Assumption.lean b/server/adam/Adam/Levels/Proposition/L02_Assumption.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Proposition/L02_Assumption.lean
rename to server/adam/Adam/Levels/Proposition/L02_Assumption.lean
index e75e141..e3101cb 100644
--- a/server/testgame/TestGame/Levels/Proposition/L02_Assumption.lean
+++ b/server/adam/Adam/Levels/Proposition/L02_Assumption.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L03_Assumption.lean b/server/adam/Adam/Levels/Proposition/L03_Assumption.lean
similarity index 82%
rename from server/testgame/TestGame/Levels/Proposition/L03_Assumption.lean
rename to server/adam/Adam/Levels/Proposition/L03_Assumption.lean
index 7a177eb..f341cbc 100644
--- a/server/testgame/TestGame/Levels/Proposition/L03_Assumption.lean
+++ b/server/adam/Adam/Levels/Proposition/L03_Assumption.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Data.Nat.Basic -- TODO
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 4
 
@@ -22,9 +22,9 @@ Statement ""
 
 **Robo** Ja.  Da kommst Du jetzt selbst drauf, wie das geht, oder?
 "
-  Hint (hidden := true) "Ist doch genau wie eben:
+  Hint (hidden := true) "**Robo**: Ist doch genau wie eben:
 die Aussage, die zu beweisen ist, gehört selbst zu den Annahmen.
-Also wird `asumption` auch wieder funktionieren."
+Also wird `assumption` auch wieder funktionieren."
   assumption
 
 Conclusion
diff --git a/server/testgame/TestGame/Levels/Proposition/L04_True.lean b/server/adam/Adam/Levels/Proposition/L04_True.lean
similarity index 94%
rename from server/testgame/TestGame/Levels/Proposition/L04_True.lean
rename to server/adam/Adam/Levels/Proposition/L04_True.lean
index 0549e7c..2be1ea1 100644
--- a/server/testgame/TestGame/Levels/Proposition/L04_True.lean
+++ b/server/adam/Adam/Levels/Proposition/L04_True.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 5
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L05_Not.lean b/server/adam/Adam/Levels/Proposition/L05_Not.lean
similarity index 93%
rename from server/testgame/TestGame/Levels/Proposition/L05_Not.lean
rename to server/adam/Adam/Levels/Proposition/L05_Not.lean
index dc1d413..486072f 100644
--- a/server/testgame/TestGame/Levels/Proposition/L05_Not.lean
+++ b/server/adam/Adam/Levels/Proposition/L05_Not.lean
@@ -1,6 +1,6 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 6
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L06_False.lean b/server/adam/Adam/Levels/Proposition/L06_False.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Proposition/L06_False.lean
rename to server/adam/Adam/Levels/Proposition/L06_False.lean
index 27d0da1..7f9ebb1 100644
--- a/server/testgame/TestGame/Levels/Proposition/L06_False.lean
+++ b/server/adam/Adam/Levels/Proposition/L06_False.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 7
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L07_ContraNotEq.lean b/server/adam/Adam/Levels/Proposition/L07_ContraNotEq.lean
similarity index 91%
rename from server/testgame/TestGame/Levels/Proposition/L07_ContraNotEq.lean
rename to server/adam/Adam/Levels/Proposition/L07_ContraNotEq.lean
index a7193df..c941a88 100644
--- a/server/testgame/TestGame/Levels/Proposition/L07_ContraNotEq.lean
+++ b/server/adam/Adam/Levels/Proposition/L07_ContraNotEq.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 8
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L08_Contra.lean b/server/adam/Adam/Levels/Proposition/L08_Contra.lean
similarity index 90%
rename from server/testgame/TestGame/Levels/Proposition/L08_Contra.lean
rename to server/adam/Adam/Levels/Proposition/L08_Contra.lean
index 296444e..94f4aa4 100644
--- a/server/testgame/TestGame/Levels/Proposition/L08_Contra.lean
+++ b/server/adam/Adam/Levels/Proposition/L08_Contra.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 9
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L09_And.lean b/server/adam/Adam/Levels/Proposition/L09_And.lean
similarity index 93%
rename from server/testgame/TestGame/Levels/Proposition/L09_And.lean
rename to server/adam/Adam/Levels/Proposition/L09_And.lean
index 773259e..3ba43a8 100644
--- a/server/testgame/TestGame/Levels/Proposition/L09_And.lean
+++ b/server/adam/Adam/Levels/Proposition/L09_And.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 10
 
@@ -12,12 +12,12 @@ Title "Und"
 Introduction
 "
 Der nächste Formalosoph in der Reihe hat seine Frage bereìts mitgebracht.
-Er legt sie uns vor, setzt sich hin, und häkelt.
+Er legt sie uns vor, setzt sich hin und häkelt.
 "
 Statement "" (A B : Prop) (hA : A) (hB : B) : A ∧ B := by
   Hint
 "
-**Du**:  Also, wir haben zwei Annahmen: `{A}` gilt, und `{B}` gilt. Auch. Und beweisen sollen wir
+**Du**:  Also, wir haben zwei Annahmen: `{A}` gilt, und `{B}` gilt auch. Und beweisen sollen wir
 dass `{A} und {B}` gilt.  Ich glaube, diese Formalospinner treiben mich noch zur Verzweiflung.
 Kann ich nicht wieder `trivial` sagen?
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L10_And.lean b/server/adam/Adam/Levels/Proposition/L10_And.lean
similarity index 96%
rename from server/testgame/TestGame/Levels/Proposition/L10_And.lean
rename to server/adam/Adam/Levels/Proposition/L10_And.lean
index c73dac6..0d4de0a 100644
--- a/server/testgame/TestGame/Levels/Proposition/L10_And.lean
+++ b/server/adam/Adam/Levels/Proposition/L10_And.lean
@@ -1,9 +1,9 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 11
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L11_Or.lean b/server/adam/Adam/Levels/Proposition/L11_Or.lean
similarity index 95%
rename from server/testgame/TestGame/Levels/Proposition/L11_Or.lean
rename to server/adam/Adam/Levels/Proposition/L11_Or.lean
index 0c5878b..b3642a9 100644
--- a/server/testgame/TestGame/Levels/Proposition/L11_Or.lean
+++ b/server/adam/Adam/Levels/Proposition/L11_Or.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
 --set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 12
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L12_Or.lean b/server/adam/Adam/Levels/Proposition/L12_Or.lean
similarity index 99%
rename from server/testgame/TestGame/Levels/Proposition/L12_Or.lean
rename to server/adam/Adam/Levels/Proposition/L12_Or.lean
index 90aa1b1..8c6959c 100644
--- a/server/testgame/TestGame/Levels/Proposition/L12_Or.lean
+++ b/server/adam/Adam/Levels/Proposition/L12_Or.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
@@ -7,7 +7,7 @@ set_option tactic.hygienic false
 --set_option autoImplicit false
 
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 13
 
diff --git a/server/testgame/TestGame/Levels/Proposition/L13_Summary.lean b/server/adam/Adam/Levels/Proposition/L13_Summary.lean
similarity index 98%
rename from server/testgame/TestGame/Levels/Proposition/L13_Summary.lean
rename to server/adam/Adam/Levels/Proposition/L13_Summary.lean
index 6db6c77..8d4c151 100644
--- a/server/testgame/TestGame/Levels/Proposition/L13_Summary.lean
+++ b/server/adam/Adam/Levels/Proposition/L13_Summary.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Std.Tactic.RCases
 import Mathlib.Tactic.LeftRight
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Proposition"
 Level 14
 
diff --git a/server/adam/Adam/Levels/SetFunction.lean b/server/adam/Adam/Levels/SetFunction.lean
new file mode 100644
index 0000000..a6f2b4b
--- /dev/null
+++ b/server/adam/Adam/Levels/SetFunction.lean
@@ -0,0 +1,8 @@
+import Adam.Levels.SetFunction.L01_Image
+import Adam.Levels.SetFunction.L02_Preimage
+import Adam.Levels.SetFunction.L03_Range
+import Adam.Levels.SetFunction.L04_ImageUnion
+
+Game "Adam"
+World "SetFunction"
+Title "Abbildungen 2"
diff --git a/server/testgame/TestGame/Levels/SetFunction/L01_Image.lean b/server/adam/Adam/Levels/SetFunction/L01_Image.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/SetFunction/L01_Image.lean
rename to server/adam/Adam/Levels/SetFunction/L01_Image.lean
index 1bfede9..9d0dbd6 100644
--- a/server/testgame/TestGame/Levels/SetFunction/L01_Image.lean
+++ b/server/adam/Adam/Levels/SetFunction/L01_Image.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetFunction"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/SetFunction/L02_Preimage.lean b/server/adam/Adam/Levels/SetFunction/L02_Preimage.lean
similarity index 83%
rename from server/testgame/TestGame/Levels/SetFunction/L02_Preimage.lean
rename to server/adam/Adam/Levels/SetFunction/L02_Preimage.lean
index b94e605..4f37c77 100644
--- a/server/testgame/TestGame/Levels/SetFunction/L02_Preimage.lean
+++ b/server/adam/Adam/Levels/SetFunction/L02_Preimage.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetFunction"
 Level 2
 
diff --git a/server/testgame/TestGame/Levels/SetFunction/L03_Range.lean b/server/adam/Adam/Levels/SetFunction/L03_Range.lean
similarity index 83%
rename from server/testgame/TestGame/Levels/SetFunction/L03_Range.lean
rename to server/adam/Adam/Levels/SetFunction/L03_Range.lean
index 21d2ccc..4809e8f 100644
--- a/server/testgame/TestGame/Levels/SetFunction/L03_Range.lean
+++ b/server/adam/Adam/Levels/SetFunction/L03_Range.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetFunction"
 Level 3
 
diff --git a/server/testgame/TestGame/Levels/SetFunction/L04_ImageUnion.lean b/server/adam/Adam/Levels/SetFunction/L04_ImageUnion.lean
similarity index 83%
rename from server/testgame/TestGame/Levels/SetFunction/L04_ImageUnion.lean
rename to server/adam/Adam/Levels/SetFunction/L04_ImageUnion.lean
index 7bfcfca..ccf1c7a 100644
--- a/server/testgame/TestGame/Levels/SetFunction/L04_ImageUnion.lean
+++ b/server/adam/Adam/Levels/SetFunction/L04_ImageUnion.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetFunction"
 Level 4
 
diff --git a/server/adam/Adam/Levels/SetTheory.lean b/server/adam/Adam/Levels/SetTheory.lean
new file mode 100644
index 0000000..59ca233
--- /dev/null
+++ b/server/adam/Adam/Levels/SetTheory.lean
@@ -0,0 +1,43 @@
+import Adam.Levels.SetTheory.L01_Univ
+import Adam.Levels.SetTheory.L02_Empty
+import Adam.Levels.SetTheory.L03_Subset
+import Adam.Levels.SetTheory.L04_SubsetEmpty
+import Adam.Levels.SetTheory.L05_Empty
+import Adam.Levels.SetTheory.L06_Nonempty
+import Adam.Levels.SetTheory.L07_UnionInter
+import Adam.Levels.SetTheory.L08_UnionInter
+import Adam.Levels.SetTheory.L09_Complement
+import Adam.Levels.SetTheory.L10_Morgan
+import Adam.Levels.SetTheory.L11_SSubset
+import Adam.Levels.SetTheory.L12_Insert
+import Adam.Levels.SetTheory.L13_Insert
+import Adam.Levels.SetTheory.L14_SetOf
+import Adam.Levels.SetTheory.L15_Powerset
+import Adam.Levels.SetTheory.L16_Disjoint
+import Adam.Levels.SetTheory.L17_SetOf
+import Adam.Levels.SetTheory.L18_SetOf
+import Adam.Levels.SetTheory.L19_Subtype
+
+
+Game "Adam"
+World "SetTheory"
+Title "Mengenlehre"
+
+Introduction
+"Der größere der beiden Monde sieht dunkelrot und karg aus. Trotzdem sollen dort nomadische
+Gesellschaften wohnen, die sich in der Einöde zurechtfinden.
+
+Ihr steuert einen der wenigen befestigten Standorte am Fusse eines Berges an.
+
+**Robo**: Die Bevölkerung hier lebt so abgekapselt vom Rest des Universums, dass sie sich
+vermutlich noch viel besser mit alter Sprache und Schrift auskennt.
+
+**Du**: Hoffen wir, dass sie uns weiterhelfen können dieses Buch der Urbilder zu entschlüsseln.
+
+Sofort begrüßt euch eine ältere Frau, die sich als *Mengea*, die Beschützerin des Mondes,
+vorstellt.
+"
+
+Game "Adam"
+World "SetTheory2"
+Title "Mehr Mengenlehre"
diff --git a/server/adam/Adam/Levels/SetTheory/L01_Univ.lean b/server/adam/Adam/Levels/SetTheory/L01_Univ.lean
new file mode 100644
index 0000000..f192095
--- /dev/null
+++ b/server/adam/Adam/Levels/SetTheory/L01_Univ.lean
@@ -0,0 +1,57 @@
+import Adam.Metadata
+
+import Mathlib.Init.Set
+import Mathlib.Tactic.Tauto
+
+set_option tactic.hygienic false
+set_option autoImplicit false
+
+Game "Adam"
+World "SetTheory"
+Level 1
+
+Title "Mengen"
+
+Introduction
+"
+**Mengea**: Ich würde leider den Inhalt jenes Buches eh nicht verstehen. Aber der beste Weg für
+euch, dieses zu entschlüsseln ist, euch ausgiebig mit der Bevölkerung hier zu unterhalten.
+Lebt mit ihnen, redet mit ihnen und ihr werdet die Sprache automatisch lernen.
+
+**Mengea**: Seit aber vorgewarnt, die Leute hier denken ganz viel über Mengen nach,
+womit sie immer *homogene Mengen* meinen. Eine Menge natürlicher Zahlen `{1, 4, 6}` ist
+verständlich, aber sowas wie eine Menge `{(2 : ℕ), {3, 1}, \"e\", (1 : ℂ)}` gibt es hier
+einfach nicht. Punkt.
+
+**Robo**: Als Kontext: Wenn `A` ein beliebiger `Type` ist, dann ist `(U : Set A)` eine Menge
+mit Elementen aus `A`
+
+**Mengea**: Damit ich weiss, dass ihr euch grundsätzlich mit den Leuten austauschen könnt,
+erklärt mir doch folgendes:
+"
+
+open Set
+
+Statement mem_univ "" {A : Type} (x : A) : x ∈ (univ : Set A) := by
+  Hint "**Du**: Also `A` ist ein `Type`, `x` ist ein Element in `A`…
+
+  **Robo** … und `univ` ist die Menge aller Elemente in `A`.
+
+  **Du** ist das nicht einfach `A` selber?
+
+  **Robo** Fast, aber das eine ist ein `Type`, das andere eine Menge, also vom Typ `Set A`.
+
+  **Du**: Unlogisch.
+
+  **Mengites**: Naja, Typen und Mengen sind halt zwei unterschiedliche Sachen und wenn ihr
+  über Mengen sprechen wollt, müssen alles Mengen sein.
+
+  **Du**: Na gut. Und wieso `x ∈ univ` und nicht `x : univ` wie bei Typen?
+
+  **Robo**: Jedes Element `(x : A)` hat entweder die Eigenschaft `x ∈ U` oder `x ∉ U` für eine
+  Menge `(U : Set A)`. (`\\in`, `\\nin`)
+
+  **Du**: Also das ist ja dann `trivial`. Hoffentlich sehen die das hier auch so…"
+  trivial
+
+Conclusion "**Mengea**: Ja das stimmt schon. Dann wünsche ich euch viel Erfolg auf eurer Reise!"
diff --git a/server/testgame/TestGame/Levels/SetTheory/L02_Empty.lean b/server/adam/Adam/Levels/SetTheory/L02_Empty.lean
similarity index 53%
rename from server/testgame/TestGame/Levels/SetTheory/L02_Empty.lean
rename to server/adam/Adam/Levels/SetTheory/L02_Empty.lean
index 193a6a6..1840659 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L02_Empty.lean
+++ b/server/adam/Adam/Levels/SetTheory/L02_Empty.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Init.Set
 import Mathlib.Tactic.Tauto
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 2
 
@@ -20,15 +20,16 @@ open Set
 
 Statement not_mem_empty "" {A : Type} (x : A) :
     x ∉ (∅ : Set A) := by
-  tauto
-
-NewLemma mem_univ
+  Hint "**Du**: Kein Element ist in der leeren Menge enthalten? Das ist ja alles
+  tautologisches Zeugs...
 
-Hint (A : Type) (x : A) : x ∉ (∅ : Set A) =>
-"**Du**: Kein Element ist in der leeren Menge enthalten? Das ist ja alles tautologisches Zeugs...
+  **Robo**: Dann behaupte das doch."
+  tauto
 
-**Robo**: Dann behaupte das doch. (`\\empty`)"
+NewLemma Set.mem_univ
 
 Conclusion "Der Junge rennt weiter.
 
-**Du**: So wird das ganze schon angenehmer."
+**Du**: So wird das ganze schon angenehmer.
+
+**Robo**: Die Leere Menge schreibst du mit `\\empty` falls du die nochmals brauchst."
diff --git a/server/adam/Adam/Levels/SetTheory/L03_Subset.lean b/server/adam/Adam/Levels/SetTheory/L03_Subset.lean
new file mode 100644
index 0000000..f87406a
--- /dev/null
+++ b/server/adam/Adam/Levels/SetTheory/L03_Subset.lean
@@ -0,0 +1,49 @@
+import Adam.Metadata
+
+import Mathlib.Init.Set
+import Mathlib.Tactic.Tauto
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "SetTheory"
+Level 3
+
+Title "Teilmengen"
+
+Introduction
+"
+Ihr bemerkt, dass mit dem Jungen noch zwei andere
+Kinder zuhörten. Eines der beiden Mädchen hat ebenfalls eine Frage.
+"
+
+-- Hat man zwei Mengen `(A B : Set ℕ)` kann man fragen, ob diese Teilmengen
+-- voneinander sind: `A ⊆ B` (`\\sub`/`\\ss`) ist die Notation für Teilmengen, die auch gleich
+-- sein können.
+
+-- `A ⊆ B` ist als `∀ x, x ∈ A → x ∈ B` definiert, das heisst, ein `⊆` kann immer auch mit `intro x hx`
+-- angegangen werden.
+
+-- Die Taktik `tauto` macht das automatisch, aber um dies zu lernen ist `tauto` hier deaktiviert.
+-- Benutze also `intro`:
+
+namespace MySet
+
+open Set
+
+Statement (A : Set ℕ) : A ⊆ univ := by
+  Hint "**Robo**: `A ⊆ B` ist als `∀ x, x ∈ A → x ∈ B` definiert.
+
+  **Du**: Also kann ich mit `intro` anfangen, wie ich das bei einem `∀` funktioniert?
+
+  **Robo**: Das ist korrekt."
+  intro h hA
+  Hint (hidden := true) "**Robo**: Das dürfte eine Trivialität sein."
+  trivial --apply mem_univ -- or `trivial`.
+
+DisabledTactic tauto simp
+NewDefinition Symbol.Subset
+
+Conclusion "Damit drehen sich die beiden Mädchen um und folgen dem Jungen."
+
+end MySet
diff --git a/server/testgame/TestGame/Levels/SetTheory/L04_SubsetEmpty.lean b/server/adam/Adam/Levels/SetTheory/L04_SubsetEmpty.lean
similarity index 56%
rename from server/testgame/TestGame/Levels/SetTheory/L04_SubsetEmpty.lean
rename to server/adam/Adam/Levels/SetTheory/L04_SubsetEmpty.lean
index d8a6990..9889ea6 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L04_SubsetEmpty.lean
+++ b/server/adam/Adam/Levels/SetTheory/L04_SubsetEmpty.lean
@@ -1,12 +1,13 @@
-import TestGame.Metadata
-import TestGame.Levels.SetTheory.L03_Subset
+import Adam.Metadata
+import Adam.Levels.SetTheory.L03_Subset
 
 import Mathlib.Init.Set
 import Mathlib.Tactic.Tauto
+import Mathlib
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 4
 
@@ -14,10 +15,14 @@ Title "Teilmengen"
 
 Introduction
 "
+Etwas weiter kommt ihr an einem kleinen Gemüsestand vorbei. Da ihr nicht so
+richtig einen Plan habt, fragt ihr den Verkäufer.
+
+**Verkäufer**: Hier ist was ganz wichtiges, was ihr noch oft brauchen werdet:
 Ein zentrales Lemma ist `Subset.antisymm_iff` welches folgendes sagt:
 
 ```
-A = B ↔ A ⊆ B ∧ B ⊆ A
+lemma antisymm_iff {α : Type} {A B : Set α} : A = B ↔ A ⊆ B ∧ B ⊆ A
 ```
 
 Fast immer wenn man Gleichheiten von Mengen zeigen muss, will man diese in zwei Ungleichungen
@@ -26,7 +31,7 @@ aufteilen.
 
 namespace MySet
 
-open Set
+open Set Subset
 
 -- Copied some lemmas from `Matlib.Data.Set.Basic` in order to not import the entire file.
 theorem tmp {α : Type _} {s t : Set α} : s = t → s ⊆ t :=
@@ -39,14 +44,17 @@ theorem Subset.antisymm_iff {α : Type _} {a b : Set α} : a = b ↔ a ⊆ b ∧
 theorem empty_subset {α : Type _} (s : Set α) : ∅ ⊆ s :=
   fun.
 
-Statement subset_empty_iff
-"Die einzige Teilmenge der leeren Menge ist die leere Menge."
-    {A : Type _} (s : Set A) :
+Statement subset_empty_iff {A : Type _} (s : Set A) :
     s ⊆ ∅ ↔ s = ∅ := by
+  Hint "**Du**: Ja, die einzige Teilmenge der leeren Menge ist die leere Menge.
+  Das ist doch eine Tautologie?
+
+  **Robo**: Ja schon, aber zuerst einmal explizit."
+  Hint (hidden := true) "**Robo**: Fang doch einmal mit `constructor` an."
   constructor
   intro h
-  rw [Subset.antisymm_iff]
-  constructor
+  Hint "**Robo**: "
+  apply Subset.antisymm
   assumption
   simp only [empty_subset]
   intro a
@@ -54,8 +62,7 @@ Statement subset_empty_iff
   rcases a with ⟨h₁, h₂⟩
   assumption
 
-NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
+DisabledTactic tauto
+NewLemma Subset.antisymm Subset.antisymm_iff empty_subset
 
 end MySet
diff --git a/server/testgame/TestGame/Levels/SetTheory/L05_Empty.lean b/server/adam/Adam/Levels/SetTheory/L05_Empty.lean
similarity index 88%
rename from server/testgame/TestGame/Levels/SetTheory/L05_Empty.lean
rename to server/adam/Adam/Levels/SetTheory/L05_Empty.lean
index 15f6394..f284019 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L05_Empty.lean
+++ b/server/adam/Adam/Levels/SetTheory/L05_Empty.lean
@@ -1,5 +1,5 @@
-import TestGame.Metadata
-import TestGame.Levels.SetTheory.L04_SubsetEmpty
+import Adam.Metadata
+import Adam.Levels.SetTheory.L04_SubsetEmpty
 
 --import Mathlib.Data.Set.Basic
 import Mathlib.Init.Set
@@ -8,7 +8,7 @@ import Mathlib.Tactic.PushNeg
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 5
 
@@ -47,6 +47,4 @@ Statement eq_empty_iff_forall_not_mem
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
 
-NewLemma Subset.antisymm_iff empty_subset
-
 end MySet
diff --git a/server/testgame/TestGame/Levels/SetTheory/L06_Nonempty.lean b/server/adam/Adam/Levels/SetTheory/L06_Nonempty.lean
similarity index 83%
rename from server/testgame/TestGame/Levels/SetTheory/L06_Nonempty.lean
rename to server/adam/Adam/Levels/SetTheory/L06_Nonempty.lean
index bc69079..a55b084 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L06_Nonempty.lean
+++ b/server/adam/Adam/Levels/SetTheory/L06_Nonempty.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
-import TestGame.Levels.SetTheory.L05_Empty
+import Adam.Metadata
+import Adam.Levels.SetTheory.L05_Empty
 
 import Mathlib.Data.Set.Basic
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 6
 
@@ -31,5 +31,3 @@ Statement nonempty_iff_ne_empty
   rfl
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L07_UnionInter.lean b/server/adam/Adam/Levels/SetTheory/L07_UnionInter.lean
similarity index 86%
rename from server/testgame/TestGame/Levels/SetTheory/L07_UnionInter.lean
rename to server/adam/Adam/Levels/SetTheory/L07_UnionInter.lean
index 098ca27..31f8c1d 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L07_UnionInter.lean
+++ b/server/adam/Adam/Levels/SetTheory/L07_UnionInter.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 7
 
@@ -27,5 +27,3 @@ Statement
   simp
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L08_UnionInter.lean b/server/adam/Adam/Levels/SetTheory/L08_UnionInter.lean
similarity index 87%
rename from server/testgame/TestGame/Levels/SetTheory/L08_UnionInter.lean
rename to server/adam/Adam/Levels/SetTheory/L08_UnionInter.lean
index 906bac4..072434b 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L08_UnionInter.lean
+++ b/server/adam/Adam/Levels/SetTheory/L08_UnionInter.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 8
 
@@ -31,5 +31,3 @@ Statement
   rw [univ_union]
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L09_Complement.lean b/server/adam/Adam/Levels/SetTheory/L09_Complement.lean
similarity index 87%
rename from server/testgame/TestGame/Levels/SetTheory/L09_Complement.lean
rename to server/adam/Adam/Levels/SetTheory/L09_Complement.lean
index f454337..0635df4 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L09_Complement.lean
+++ b/server/adam/Adam/Levels/SetTheory/L09_Complement.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 9
 
@@ -31,5 +31,3 @@ Statement
   exact h4
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L10_Morgan.lean b/server/adam/Adam/Levels/SetTheory/L10_Morgan.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/SetTheory/L10_Morgan.lean
rename to server/adam/Adam/Levels/SetTheory/L10_Morgan.lean
index 76b6900..db12481 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L10_Morgan.lean
+++ b/server/adam/Adam/Levels/SetTheory/L10_Morgan.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 10
 
diff --git a/server/testgame/TestGame/Levels/SetTheory/L11_SSubset.lean b/server/adam/Adam/Levels/SetTheory/L11_SSubset.lean
similarity index 90%
rename from server/testgame/TestGame/Levels/SetTheory/L11_SSubset.lean
rename to server/adam/Adam/Levels/SetTheory/L11_SSubset.lean
index 6dd11f4..e587290 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L11_SSubset.lean
+++ b/server/adam/Adam/Levels/SetTheory/L11_SSubset.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib.Data.Set.Basic
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 11
 
@@ -34,5 +34,3 @@ Statement
   exact hx
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L12_Insert.lean b/server/adam/Adam/Levels/SetTheory/L12_Insert.lean
similarity index 91%
rename from server/testgame/TestGame/Levels/SetTheory/L12_Insert.lean
rename to server/adam/Adam/Levels/SetTheory/L12_Insert.lean
index 40c786d..6996503 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L12_Insert.lean
+++ b/server/adam/Adam/Levels/SetTheory/L12_Insert.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 12
 
@@ -33,5 +33,3 @@ Statement
   rfl
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L13_Insert.lean b/server/adam/Adam/Levels/SetTheory/L13_Insert.lean
similarity index 95%
rename from server/testgame/TestGame/Levels/SetTheory/L13_Insert.lean
rename to server/adam/Adam/Levels/SetTheory/L13_Insert.lean
index cb32a1a..30ab7d8 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L13_Insert.lean
+++ b/server/adam/Adam/Levels/SetTheory/L13_Insert.lean
@@ -1,8 +1,8 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 13
 
diff --git a/server/testgame/TestGame/Levels/SetTheory/L14_SetOf.lean b/server/adam/Adam/Levels/SetTheory/L14_SetOf.lean
similarity index 89%
rename from server/testgame/TestGame/Levels/SetTheory/L14_SetOf.lean
rename to server/adam/Adam/Levels/SetTheory/L14_SetOf.lean
index 50a1e18..e0fcc3c 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L14_SetOf.lean
+++ b/server/adam/Adam/Levels/SetTheory/L14_SetOf.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 1
 
@@ -33,5 +33,3 @@ Statement
   ring
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L15_Powerset.lean b/server/adam/Adam/Levels/SetTheory/L15_Powerset.lean
similarity index 88%
rename from server/testgame/TestGame/Levels/SetTheory/L15_Powerset.lean
rename to server/adam/Adam/Levels/SetTheory/L15_Powerset.lean
index 7162728..9c8acc9 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L15_Powerset.lean
+++ b/server/adam/Adam/Levels/SetTheory/L15_Powerset.lean
@@ -1,12 +1,12 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 2
 
@@ -38,5 +38,3 @@ Statement
 
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L16_Disjoint.lean b/server/adam/Adam/Levels/SetTheory/L16_Disjoint.lean
similarity index 90%
rename from server/testgame/TestGame/Levels/SetTheory/L16_Disjoint.lean
rename to server/adam/Adam/Levels/SetTheory/L16_Disjoint.lean
index df5d23e..5cf6745 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L16_Disjoint.lean
+++ b/server/adam/Adam/Levels/SetTheory/L16_Disjoint.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib
 import Mathlib.Algebra.Parity
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 3
 
@@ -37,5 +37,3 @@ Statement
 
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L17_SetOf.lean b/server/adam/Adam/Levels/SetTheory/L17_SetOf.lean
similarity index 86%
rename from server/testgame/TestGame/Levels/SetTheory/L17_SetOf.lean
rename to server/adam/Adam/Levels/SetTheory/L17_SetOf.lean
index 94d3ae8..80b1bb2 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L17_SetOf.lean
+++ b/server/adam/Adam/Levels/SetTheory/L17_SetOf.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 4
 
@@ -35,5 +35,3 @@ Statement
 
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L18_SetOf.lean b/server/adam/Adam/Levels/SetTheory/L18_SetOf.lean
similarity index 87%
rename from server/testgame/TestGame/Levels/SetTheory/L18_SetOf.lean
rename to server/adam/Adam/Levels/SetTheory/L18_SetOf.lean
index 5d81257..211ec53 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L18_SetOf.lean
+++ b/server/adam/Adam/Levels/SetTheory/L18_SetOf.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 5
 
@@ -29,5 +29,3 @@ Statement
   library_search
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L19_Subtype.lean b/server/adam/Adam/Levels/SetTheory/L19_Subtype.lean
similarity index 78%
rename from server/testgame/TestGame/Levels/SetTheory/L19_Subtype.lean
rename to server/adam/Adam/Levels/SetTheory/L19_Subtype.lean
index 93569fb..20d82c2 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L19_Subtype.lean
+++ b/server/adam/Adam/Levels/SetTheory/L19_Subtype.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 6
 
@@ -24,5 +24,3 @@ Statement
   ring
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L20_UnionInter.lean b/server/adam/Adam/Levels/SetTheory/L20_UnionInter.lean
similarity index 82%
rename from server/testgame/TestGame/Levels/SetTheory/L20_UnionInter.lean
rename to server/adam/Adam/Levels/SetTheory/L20_UnionInter.lean
index 7a9d10e..132da70 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L20_UnionInter.lean
+++ b/server/adam/Adam/Levels/SetTheory/L20_UnionInter.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory2"
 Level 7
 
@@ -23,5 +23,3 @@ Statement
 "" : True := sorry
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/L21_Summary.lean b/server/adam/Adam/Levels/SetTheory/L21_Summary.lean
similarity index 78%
rename from server/testgame/TestGame/Levels/SetTheory/L21_Summary.lean
rename to server/adam/Adam/Levels/SetTheory/L21_Summary.lean
index 52d376c..83e645c 100644
--- a/server/testgame/TestGame/Levels/SetTheory/L21_Summary.lean
+++ b/server/adam/Adam/Levels/SetTheory/L21_Summary.lean
@@ -1,10 +1,10 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Parity
 import Mathlib.Tactic.Ring
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 21
 
@@ -24,5 +24,3 @@ Statement
   ring
 
 NewTactic constructor intro rw assumption rcases simp tauto trivial
-
-NewLemma Subset.antisymm_iff empty_subset
diff --git a/server/testgame/TestGame/Levels/SetTheory/PowersetPlayground.lean b/server/adam/Adam/Levels/SetTheory/PowersetPlayground.lean
similarity index 100%
rename from server/testgame/TestGame/Levels/SetTheory/PowersetPlayground.lean
rename to server/adam/Adam/Levels/SetTheory/PowersetPlayground.lean
diff --git a/server/testgame/TestGame/Levels/SetTheory/T01_Set.lean b/server/adam/Adam/Levels/SetTheory/T01_Set.lean
similarity index 99%
rename from server/testgame/TestGame/Levels/SetTheory/T01_Set.lean
rename to server/adam/Adam/Levels/SetTheory/T01_Set.lean
index f8ac55d..21e9d0b 100644
--- a/server/testgame/TestGame/Levels/SetTheory/T01_Set.lean
+++ b/server/adam/Adam/Levels/SetTheory/T01_Set.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib.Order.SymmDiff
 import Mathlib.Logic.Function.Iterate
@@ -14,7 +14,7 @@ import Mathlib
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 1
 
diff --git a/server/testgame/TestGame/Levels/SetTheory/T04_xx.lean b/server/adam/Adam/Levels/SetTheory/T04_xx.lean
similarity index 97%
rename from server/testgame/TestGame/Levels/SetTheory/T04_xx.lean
rename to server/adam/Adam/Levels/SetTheory/T04_xx.lean
index bb8523c..7d0f0ad 100644
--- a/server/testgame/TestGame/Levels/SetTheory/T04_xx.lean
+++ b/server/adam/Adam/Levels/SetTheory/T04_xx.lean
@@ -1,4 +1,4 @@
-import TestGame.Metadata
+import Adam.Metadata
 
 import Mathlib
 import Duper.Tactic
@@ -8,7 +8,7 @@ import Mathlib.Order.Disjoint
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "SetTheory"
 Level 4
 
diff --git a/server/testgame/TestGame/Levels/StatementTest.lean b/server/adam/Adam/Levels/StatementTest.lean
similarity index 93%
rename from server/testgame/TestGame/Levels/StatementTest.lean
rename to server/adam/Adam/Levels/StatementTest.lean
index 2d00bb9..db6bc7f 100644
--- a/server/testgame/TestGame/Levels/StatementTest.lean
+++ b/server/adam/Adam/Levels/StatementTest.lean
@@ -1,7 +1,7 @@
-import TestGame.Metadata
+import Adam.Metadata
 import Mathlib
 
-Game "TestGame"
+Game "Adam"
 World "TestWorld"
 Level 1
 
diff --git a/server/adam/Adam/Levels/Sum.lean b/server/adam/Adam/Levels/Sum.lean
new file mode 100644
index 0000000..5f5172b
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum.lean
@@ -0,0 +1,20 @@
+import Adam.Levels.Sum.L01_Simp
+import Adam.Levels.Sum.L02_Sum
+import Adam.Levels.Sum.L03_ArithSum
+import Adam.Levels.Sum.L04_SumOdd
+import Adam.Levels.Sum.L05_SumComm
+import Adam.Levels.Sum.L06_Summary
+
+Game "Adam"
+World "Sum"
+Title "Endliche Summe"
+
+Introduction "Mit dem Gefühl, dass sich *Evenine* und *Oddeus* in Zukunft wieder
+besser verstehen werden, steigt ihr in eurer Raumschiff und setzt eure Reise fort.
+
+Bald erreicht ihr einen neuen Planet. Die oberfläche scheint steinig zu sein, aber nicht etwa
+geröll oder Chaos. Stattdessen, scheinen unzählige Steinplatten zu bizzaren hohen Türme
+gestapelt und die ganze Landschaft wirkt wie ein grosses Puzzle in dem jede Platte
+feinsäuberlich auf den darunterliegenden Platten aufbaut.
+
+Bald trefft ihr auch die Bewohner dieses Planeten an."
diff --git a/server/adam/Adam/Levels/Sum/L01_Simp.lean b/server/adam/Adam/Levels/Sum/L01_Simp.lean
new file mode 100644
index 0000000..a735024
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum/L01_Simp.lean
@@ -0,0 +1,66 @@
+import Adam.Metadata
+
+import Adam.ToBePorted
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Sum"
+Level 1
+
+Title "Simp"
+
+Introduction
+"
+**Unbekannte**: Willkommen auf *Indu*, unserem Planeten! Bevor ich euch herumzeigen will,
+sagt mir, ob ihr unsere Lebensweise zu verstehen und schätzen wisst:
+In diesem Kapitel lernen wir endliche Summen und mehr Übungen zur Induktion.
+
+"
+
+-- Eine endliche Summe läuft erstmal immer über einen endlichen Index
+-- `Fin n`, welcher $n$ Elemente
+-- $\\{0, 1, \\ldots, n-1\\}$ beinhaltet.
+
+-- Der Syntax für  $\\sum_{i=0}^n a_i$ ist `∑ i : Fin n, _` (\\sum)
+
+-- Als erstes kann die Taktik `simp` (für \"simplification\") ganz viel Triviales vereinfachen.
+-- `simp` ist eine der stärksten Taktiken in Lean und verwendet
+-- ganz viele markierte Lemmas um das Goal zu vereinfachen.
+
+-- Zum Beispiel kennt es ein Lemma das ungefähr so aussieht:
+
+-- ```
+-- @[simp]
+-- lemma sum_const_add (n : ℕ) : (∑ i in Fin n, 0) = 0 := by
+--   sorry
+-- ```
+
+-- Die Taktik `simp` benützt alle Lemmas, die mit `@[simp]` markiert sind.
+
+-- (Tipp: `simp?` zeigt an, welche Lemmas `simp` benutzen würde.)
+
+open BigOperators
+
+Statement (n : ℕ) : (∑ i : Fin n, (0 + 0)) = 0 := by
+  Hint "BUG"
+
+  -- TODO (Bug): Invalid escape sequence:
+  -- "**Du**: Oh das ist ganz schön viel neues… Mal sehen, das sagt wohl
+  -- $( \\sum_i 0 + 0 ) = 0$. Dann ist das vielleicht doch nicht so komplex.
+
+  -- **Robo**: Genau! Man schreibt `\\sum`. Beachte den Index:
+  -- $( \\sum_\{i=0}^\{n-1} 0 + 0 ) = 0$, also `Fin n` ist ein Typ mit den Elementen
+  -- $\\{0, \\ldots, n-1\\}$.
+
+  -- **Du**: Oke, also `Fin n` hat `n` Elemente. Und was mach ich jetzt?
+
+  -- **Robo**: `simp` ist eine ganz starke Taktik, die viele Terme vereinfacht, wir
+  -- fangen besser an, diese zu benützen.
+
+  -- Irgendwie hast du das Gefühl ein Déjà-vue zu haben…"
+  simp
+
+OnlyTactic simp
+
+Conclusion "**Unbekannte**: Sehr gut, folgt mir!"
diff --git a/server/adam/Adam/Levels/Sum/L02_Sum.lean b/server/adam/Adam/Levels/Sum/L02_Sum.lean
new file mode 100644
index 0000000..65a3ad0
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum/L02_Sum.lean
@@ -0,0 +1,54 @@
+import Adam.Metadata
+
+import Adam.ToBePorted
+import Mathlib
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Sum"
+Level 2
+
+Title "endliche Summe"
+
+Introduction
+"
+Während euch die Person zu einem besonders herausragenden Steinturm führt, löchert
+sie euch noch weiter mit Fragen.
+"
+
+open BigOperators
+
+Statement
+    "$\\sum_{i=0}^{n-1} (i + 1) = n + \\sum_{i=0}^{n-1} i$."
+    (n : ℕ) : ∑ i : Fin n, ((i : ℕ) + 1) = n + (∑ i : Fin n, (i : ℕ)) := by
+  -- Hint "**Du**: Hmm, wieder `simp`?
+
+  -- **Robo**: Nicht ganz. `simp` benützt nur Lemmas, die klar eine Vereinfachung darstellen,
+  -- und in deiner Bibliothek mit `@[simp]` markiert wird. Hier brauchen wir eine andere
+  -- Umformung:
+
+  -- $$
+  -- \\sum_\{i = 0}^n a_i + b_i = \\sum_\{i = 0}^n a_i + \\sum_\{j = 0}^n b_j
+  -- $$
+
+  -- **Robo*: Da unklar ist, welche Seite \"einfacher\" ist, wird so ein Lemma nicht mit
+  -- `@[simp]` markiert. Das heisst du musst `Finset.sum_add_distrib` mit `rw`
+  -- explizit anwenden.
+  -- "
+  rw [Finset.sum_add_distrib]
+  Hint "**Robo**: Die zweite Summe `∑ x : Fin n, 1` kann jetzt aber mit
+  `simp` zu `n` vereinfacht werden."
+  simp
+  Hint "**Robo**: Bis auf Umordnung sind jetzt beide Seiten gleich!
+
+  **Du**: Dann greift jetzt wohl `ring`!
+
+  **Robo**: Genau! Und alternativ könntest du mit `rw [add_comm]` die Arbeit von `ring`
+  auch manuell machen."
+  ring
+
+NewLemma Finset.sum_add_distrib add_comm
+
+Conclusion "Eure Begleitung scheint mit der Antwort zu frieden zu sein und zeigt
+freudig an dem Turm empor, den ihr soeben erreicht habt."
diff --git a/server/adam/Adam/Levels/Sum/L03_ArithSum.lean b/server/adam/Adam/Levels/Sum/L03_ArithSum.lean
new file mode 100644
index 0000000..c87d95e
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum/L03_ArithSum.lean
@@ -0,0 +1,89 @@
+import Adam.Metadata
+
+import Mathlib.Algebra.BigOperators.Fin
+import Mathlib.Tactic.Ring
+
+import Adam.ToBePorted
+
+set_option tactic.hygienic false
+
+Game "Adam"
+World "Sum"
+Level 3
+
+Title "Arithmetische Summe"
+
+Introduction
+"
+**Du**: Wie werden solche Meisterwerke eigentlich gebaut?
+
+Da zeigt eure Begleitung auf eine kleine Steinplatte neben dem Eingang,
+auf der eien Beschreibung gekritzelt ist.
+
+**Robo**: Das ist wohl der bekannte arithmetische Turm von Indu, über den hab ich schon
+einmal Daten verarbeitet. Und die antwort auf deine Frage: Vermutlich ein Stein nach
+dem anderen.
+"
+
+open BigOperators
+
+Statement arithmetic_sum
+    "$2 \\cdot \\sum_{i = 0}^n i = n \\cdot (n + 1)$."
+    (n : ℕ) : 2 * (∑ i : Fin (n + 1), ↑i) = n * (n + 1) := by
+  Hint "**Du**: Klar, die werden ja nicht oben anfangen mit bauen. Sag mal,
+  wie zeige ich denn die arithmetische Summe, die hier gekritzelt steht?
+  Ich würde gerne Induktion über $n$ anwenden.
+
+  **Robo**: Ja dann ist's einfach `induction n`, ist doch logisch!"
+  induction n
+  Hint "**Du**: Zuerst den Induktionsanfang…
+
+  **Robo**: Diesen kannst du oft mit `simp` abkürzen!"
+  simp
+  Hint "**Robo**: Jetzt im Induktionsschritt: Bei Induktion über endlichen Summen willst du
+  immer mit `rw [Fin.sum_univ_castSucc]` anfangen" -- :
+
+  -- $$\\sum_\{i=0}^n a_i = \\sum_{i=0}^\{n-1} a_i + a_n$$"
+  rw [Fin.sum_univ_castSucc]
+  -- TODO: Bug. Dieser Hint wird nicht angezeigt.
+  Hint "**Du**: Oh das sieht jetz aber kompliziert aus…
+
+  **Robo**: Da musst du etwas drüber hinweg lesen. Am besten machst du kurz `simp`,
+  dann sieht's schon wieder besser aus."
+  simp
+  Hint "**Du**: Was bedeutet eigentlich der kleine Pfeil `↑`?
+
+  **Robo**: Das ist eine *Coersion*. Sowas wie wenn man eine natürliche Zahl als Integer anschaut,
+  also die natürliche Abbildung `ℕ ↪ ℤ`. Oder hier, wenn ein Element `x : Fin n` stattdessen als
+  Element in `(↑x : ℕ)` angeschaut wird.
+
+  **Robo**: Übrigens, um die Induktionshypothese anzuwenden brauchst du zuerst das Lemma
+  `mul_add`."
+  rw [mul_add]
+  Hint "**Du**: Und wie wende ich jetzt die Induktionshypothese an?
+
+  **Robo mit `rw` wie jede andere Annahme auch."
+  rw [n_ih]
+  Hint "**Robo**: Jetzt musst du noch kurz `rw [Nat.succ_eq_add_one]` anwenden.
+
+  **Du**: Aber wieso?
+
+  **Robo**: Naja, `ring` ist jetzt auch noch nicht so stark, und erkennt nicht dass `n.succ`
+  und `n + 1` das gleiche sind.
+
+  **Du**: Aber das könnte man doch ändern, oder?
+
+  **Robo**: Vielleicht wenn wir einmal einem Techniker begegnen, der mir ein Update
+  einspielen kann…"
+  Branch
+    ring_nf
+    Hint "**Robo**: Wie gesagt, brauch doch `rw [Nat.succ_eq_add_one]` als Fix für meine
+    kleinen Maken."
+  rw [Nat.succ_eq_add_one]
+  ring
+
+NewTactic induction
+NewLemma Fin.sum_univ_castSucc Nat.succ_eq_add_one mul_add add_mul Nat.zero_eq
+
+Conclusion "Du schaust dich um und bewunderst das Tal in dem hunderte, wenn nicht tausende,
+Steintürme in allen Formen und Höhen stehen."
diff --git a/server/adam/Adam/Levels/Sum/L04_SumOdd.lean b/server/adam/Adam/Levels/Sum/L04_SumOdd.lean
new file mode 100644
index 0000000..d84dd40
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum/L04_SumOdd.lean
@@ -0,0 +1,33 @@
+import Adam.Metadata
+
+import Adam.ToBePorted
+import Mathlib.Algebra.BigOperators.Fin
+import Mathlib.Tactic.Ring
+
+Game "Adam"
+World "Sum"
+Level 4
+
+Title "Summe aller ungeraden Zahlen"
+
+Introduction
+"
+**Du**: Haben eigentlich alle Türme hier so kryptische Beschreibungen am Eingang?
+
+Du gehst zu einem etwas kleineren Nachbarsturm.
+"
+set_option tactic.hygienic false
+
+open BigOperators
+
+Statement odd_arithmetic_sum
+    "$\\sum_{i = 0}^n (2n + 1) = n ^ 2$."
+    (n : ℕ) : (∑ i : Fin n, (2 * (i : ℕ) + 1)) = n ^ 2 := by
+  Hint "**Robo**: Das funktioniert genau gleich wie zuvor, viel Glück."
+  induction n
+  simp
+  rw [Fin.sum_univ_castSucc]
+  simp
+  rw [n_ih]
+  rw [Nat.succ_eq_add_one]
+  ring
diff --git a/server/adam/Adam/Levels/Sum/L05_SumComm.lean b/server/adam/Adam/Levels/Sum/L05_SumComm.lean
new file mode 100644
index 0000000..dd5cc37
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum/L05_SumComm.lean
@@ -0,0 +1,49 @@
+import Adam.Metadata
+
+import Adam.ToBePorted
+import Mathlib.Algebra.BigOperators.Fin
+import Mathlib.Tactic.Ring
+
+import Adam.Options.ArithSum
+
+set_option tactic.hygienic false
+
+open BigOperators
+
+Game "Adam"
+World "Sum"
+Level 5
+
+Title "Summe vertauschen"
+
+Introduction
+"
+Nun aber zeigt euch eure Begleiterin zwei weitere Türme mit einer kleinen Brücke, die
+zwischen den beiden verläuft. Die Tafel am Eingang wurde von einem herunterfallenden Stein
+zerstört. Auf der oberen Hälfte steht nur folgendes:
+
+$$\\sum_{i=0}^n\\sum_{j=0}^m a_{ij} = \\sum_{j=0}^m\\sum_{i=0}^n a_{ij}$$
+
+**Du**: Ich glaube, ich kann das in eurem Dialekt formulieren und euch damit helfen!
+"
+
+
+Statement
+(n m : ℕ) : ∑ i : Fin n, ∑ j : Fin m, ( 2^i * (1 + j) : ℕ) =
+    ∑ j : Fin m, ∑ i : Fin n, ( 2^i * (1 + j) : ℕ) := by
+  Hint "**Robo**: Das sieht gut aus, aber du solltest das kurz beweisen, um sicher zu sein.
+
+  **Du**: Hast du nicht ein Lemma dafür?
+
+  **Robo**: Doch, probier mal `Finset.sum_comm`."
+  rw [Finset.sum_comm]
+
+NewLemma Finset.sum_comm
+
+Conclusion "
+  Euer Begleiter ist ganz begeistert als er dir das Stück Papier aus den Händen nimmt,
+  auf dem du die Aussage gekritzelt hast. Gleich zückt sie einen Meißel und beginnt eine
+  neue Platte zu erstellen.
+
+  Ihr winkt ihr noch zum Abschied und geht weiter.
+"
diff --git a/server/adam/Adam/Levels/Sum/L06_Summary.lean b/server/adam/Adam/Levels/Sum/L06_Summary.lean
new file mode 100644
index 0000000..45f2a13
--- /dev/null
+++ b/server/adam/Adam/Levels/Sum/L06_Summary.lean
@@ -0,0 +1,92 @@
+import Adam.Metadata
+
+import Adam.ToBePorted
+import Mathlib.Algebra.BigOperators.Fin
+import Mathlib.Tactic.Ring
+
+import Adam.ToBePorted
+import Adam.Options.ArithSum
+
+Game "Adam"
+World "Sum"
+Level 6
+
+set_option tactic.hygienic false
+
+Title "Zusammenfassung"
+
+Introduction
+"
+**Du**: Robo gib mir nochmals eine Übersicht, bitte.
+
+**Robo**: Aber klar:
+
+|                      | Beschreibung                              |
+|:---------------------|:------------------------------------------|
+| `Fin n`              | Ist ein Typ mit Zahlen $0, \\ldots, n-1$. |
+| `∑ (i : Fin n), a i` | $\\sum_{i=0}^{n-1} a_i$                   |
+| `↑i`                 | Eine Coersion, z.B. `Fin n → ℕ`.          |
+
+und
+
+|    | Taktik                    | Beispiel                             |
+|:---|:--------------------------|:-------------------------------------|
+| 21 | `simp`                    | Simplifikation.                      |
+| 22 | `induction n`             | Induktion über $n$                   |
+
+Da löst sich aus der Steinlandschaft plötzlich ein grosser Steingolem. Er schaut euch
+bedrohlich an und fragt in tiefer Stimme:
+"
+
+open BigOperators
+
+Statement (m : ℕ) : (∑ i : Fin (m + 1), (i : ℕ)^3) = (∑ i : Fin (m + 1), (i : ℕ))^2 := by
+  Hint "**Du**: Gulp. Naja das wird schon klappen. Also man fängt wieder mit Induktion an…"
+  induction m
+  Hint "**Du**: Also den Induktionsanfang kann man einfach zeigen…"
+  simp
+  Hint "**Robo**: Und jetzt wieder `rw [Fin.sum_univ_castSucc]` und `simp` um vorwärts zu
+  kommen!"
+  rw [Fin.sum_univ_castSucc]
+  simp
+  Hint "**Robo**: Siehst du die Induktionshypothese hier drin?"
+  rw [n_ih]
+  Hint "**Du**: Ok, damit habe ich die linke Seite der Gleichung ziemlich gut bearbeitet.
+  Aber, ehm, mit der Rechten komme ich nicht weiter…
+
+  Der Golem schaut dich finster an.
+
+  **Robo**: Du willst `Fin.sum_univ_castSucc` auf der rechten Seite anwenden, aber es
+  gibt mehrere Orte, wo das Lemma passen würde.
+  Deshalb musst du mit `rw [Fin.sum_univ_castSucc (n := {n} + 1)]` angeben, wo genau.
+
+  **Du**: Was bedeutet das?
+
+  **Robo** Das Lemma hat eine Annahme `n` und du sagst ihm explizit, was es für dieses `n`
+  einsetzen muss, nämlich `{n} + 1`"
+  Branch
+    rw [Fin.sum_univ_castSucc]
+    Hint "**Robo**: Das hat jetzt einfach `Fin.sum_univ_castSucc` am ersten Ort angewendet,
+    wo das möglich war. Das ist nicht so ideal, die like Seite war schon okay.
+
+    **Robo**: Geh doch zurück und bring `rw` dazu am anderen Ort umzuschreiben."
+  rw [Fin.sum_univ_castSucc (n := n + 1)]
+  simp
+  Hint "**Robo**: `add_pow_two` ist auch noch nützlich!"
+  rw [add_pow_two]
+  Hint "**Du**: Ich glaube, ich sehe hier ne arithmetische Summe drin!!
+
+  **Robo**: Ich habe dir das dies von vorhin temporär als `arithmetic_sum` gespeichert,
+  damit du diese brauchen kannst."
+  rw [arithmetic_sum]
+  Hint "**Du**: Jetzt sollten es eigentlich nur noch arithmetische Operationen sein."
+  ring
+
+NewLemma arithmetic_sum add_pow_two
+
+Conclusion "Der Golem denkt ganz lange nach, und ihr bekommt das Gefühl, dass er gar nie
+aggressive war, sondern nur eine sehr tiefe Stimme hat.
+
+Mit einem kleinen Erdbeben setzt er sich hin und winkt euch dankend zu.
+
+Damit zieht ihr weiter durch die karge Landschaft auf diesem Planet."
diff --git a/server/testgame/TestGame/Levels/Sum/T01_Induction.lean b/server/adam/Adam/Levels/Sum/T01_Induction.lean
similarity index 83%
rename from server/testgame/TestGame/Levels/Sum/T01_Induction.lean
rename to server/adam/Adam/Levels/Sum/T01_Induction.lean
index 1e2c033..24062ab 100644
--- a/server/testgame/TestGame/Levels/Sum/T01_Induction.lean
+++ b/server/adam/Adam/Levels/Sum/T01_Induction.lean
@@ -1,13 +1,13 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-import TestGame.Options.BigOperators
+import Adam.ToBePorted
 import Mathlib.Algebra.BigOperators.Fin
 
 set_option tactic.hygienic false
 
 open Nat
 
-Game "TestGame"
+Game "Adam"
 World "Sum"
 Level 2
 
@@ -36,5 +36,3 @@ example (n : ℕ) (h : 5 ≤ n) : n^2 < 2 ^ n
 | 0 | 1 | 2 | 3 | 4 => by
   sorry
 | n + 5  => by sorry
-
-NewTactic rw simp ring
diff --git a/server/testgame/TestGame/Levels/Sum/T02_Induction.lean b/server/adam/Adam/Levels/Sum/T02_Induction.lean
similarity index 85%
rename from server/testgame/TestGame/Levels/Sum/T02_Induction.lean
rename to server/adam/Adam/Levels/Sum/T02_Induction.lean
index aa25628..09f6400 100644
--- a/server/testgame/TestGame/Levels/Sum/T02_Induction.lean
+++ b/server/adam/Adam/Levels/Sum/T02_Induction.lean
@@ -1,11 +1,11 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-import TestGame.Options.BigOperators
+import Adam.ToBePorted
 import Mathlib.Algebra.BigOperators.Fin
 
 set_option tactic.hygienic false
 
-Game "TestGame"
+Game "Adam"
 World "Sum"
 Level 2
 
@@ -32,4 +32,3 @@ Statement
 --   ring
 --   rw [Nat.succ_eq_one_add]
 --   rw []
-NewTactic rw simp ring
diff --git a/server/testgame/TestGame/Levels/Sum/T03__Bernoulli.lean b/server/adam/Adam/Levels/Sum/T03__Bernoulli.lean
similarity index 88%
rename from server/testgame/TestGame/Levels/Sum/T03__Bernoulli.lean
rename to server/adam/Adam/Levels/Sum/T03__Bernoulli.lean
index 003a584..0c73287 100644
--- a/server/testgame/TestGame/Levels/Sum/T03__Bernoulli.lean
+++ b/server/adam/Adam/Levels/Sum/T03__Bernoulli.lean
@@ -1,12 +1,12 @@
-import TestGame.Metadata
+import Adam.Metadata
 
-import TestGame.Options.BigOperators
+import Adam.ToBePorted
 import Mathlib.Algebra.BigOperators.Fin
 import Mathlib.Tactic.Ring
 
-import TestGame.ToBePorted
+import Adam.ToBePorted
 
-Game "TestGame"
+Game "Adam"
 World "Sum"
 Level 5
 
diff --git a/server/testgame/TestGame/Metadata.lean b/server/adam/Adam/Metadata.lean
similarity index 63%
rename from server/testgame/TestGame/Metadata.lean
rename to server/adam/Adam/Metadata.lean
index a9fd86a..e0f2b52 100644
--- a/server/testgame/TestGame/Metadata.lean
+++ b/server/adam/Adam/Metadata.lean
@@ -1,4 +1,4 @@
 import GameServer.Commands
-import TestGame.TacticDocs
-import TestGame.LemmaDocs
+import Adam.TacticDocs
+import Adam.LemmaDocs
 import Mathlib.Init.Data.Nat.Basic -- Imports the notation ℕ.
diff --git a/server/testgame/TestGame/Options/ArithSum.lean b/server/adam/Adam/Options/ArithSum.lean
similarity index 100%
rename from server/testgame/TestGame/Options/ArithSum.lean
rename to server/adam/Adam/Options/ArithSum.lean
diff --git a/server/testgame/TestGame/Playground.lean b/server/adam/Adam/Playground.lean
similarity index 100%
rename from server/testgame/TestGame/Playground.lean
rename to server/adam/Adam/Playground.lean
diff --git a/server/adam/Adam/StructInstWithHoles.lean b/server/adam/Adam/StructInstWithHoles.lean
new file mode 100644
index 0000000..0921856
--- /dev/null
+++ b/server/adam/Adam/StructInstWithHoles.lean
@@ -0,0 +1,1698 @@
+/- Copied from `https://github.com/leanprover-community/mathlib4/tree/thorimur/refine_struct-via-StructInst` -/
+
+/-
+Copyright (c) 2020 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+import Lean.Util.FindExpr
+import Lean.Parser.Term
+import Lean.Meta.Structure
+import Lean.Elab.App
+import Lean.Elab.Binders
+
+set_option autoImplicit true
+
+/-!
+  # Structure Instances With (Variadic) Holes
+  This file defines a term elaborator for structure instance syntax that includes "variadic holes",
+  i.e. holes of "variable length", which are represented via via the syntax `?..`, `?..!`, etc.,
+  e.g. `{ x := 0, ?.. }`.
+  This serves to port the functionality of mathlib3's `refine_struct { .. }`, but via `refine`
+  (e.g. `refine { ?.. }`).
+  Lean currently already supports one form of variadic hole in structure instances, namely `..`,
+  which fills all unspecified fields with natural metavariables and which is frequently used in
+  pattern matching.
+  Variadic holes that begin with a question mark are meant to parallel named holes (e.g. `?x`).
+  Therefore, syntax like `{ x := 0, ?.. }` will fill all remaining fields with metavariables named
+  by the field in question (e.g. `y := ?y`). Identifiers can optionally be provided to prefix the
+  name; see below.
+  Tests are performed in `Tests/StructInstWithHoles.lean`.
+  At the end of this file, we implement `haveFieldProj` in analogy to `have_field` with some
+  modifications. (This might be moved or eliminated.)
+  ## Current specifics
+  The following is subject to change.
+  Several variants are supported to enable the choice between synthetic holes (`?`) and natural
+  ones, and to enable the choice between filling all unspecified fields with holes (`!`) and
+  synthesizing defaults where possible.
+  Currently only three combinations are allowed, since I can't see a use for unnamed/natural goals
+  with synthesized defaults. More descriptive syntax might be used for indicating whether to
+  synthesize defaults or not (e.g. `?.. noDefaults`)
+                synthesize defaults
+                ┌──true──┬─false──┐
+    named goals │ `?..`  │ `?..!` │
+                ├────────┼────────┤
+  unnamed goals │   ×    │  `..`  │
+                └────────┴────────┘
+  Identifiers can be provided after the variadic hole syntax in the `?` case, e.g. `?..foo` and
+  `?..!foo`. These will be prefixed to the goal name. For example, a field `y`'s goal will be named
+  `foo.y` instead of `y`.
+  # Overview of existing code
+  This document began as `StructInst.lean`, then was modified as needed. The modifications are done
+  in such a way as to (hopefully) make it easy for them to be absorbed into `StructInst.lean`, if
+  that's where it ends up. The following details how the original `StructInst.lean` works (which is
+  largely preserved).
+  ## Short version
+  The way this works is that we start with syntax, parse it into a bare-bones `Struct`, use
+  `expandStruct` to expand that struct into another struct that has intermediate indicators
+  (`FieldVal`s) holding raw syntax or accounting for its absence. We then `elabStruct` that struct
+  into an `ElabStructResult` which has the potential result expression (an application of the
+  structure's single constructor to its values, which may be metavariables if they weren't found in
+  the syntax) plus info on the original struct. We then synthesize defaults using `propagate` to
+  assign any metavariables standing in for default values, and then return the expression.
+  ## Long version
+  We start with turning the syntax into a struct. First we extract the sources (everything before
+  the `with` and any variadic holes (`..` or similar)), then we feed this to `elabStructInstAux`
+  along with the raw syntax and expected type. Inside `elabStructInstAux` we make the syntax into a
+  Struct (`mkStructView`), then `expandStruct`.
+  There's a "pre-expression scaffolding/framework/spine" set up early on in the process in the form
+  of FieldVal's, which hold raw information: `.term stx` where `stx` is syntax, if a term was
+  provided; a `.missing` value if it was missing; or a `.nested s` value where `s` is a `Struct` if
+  a subobject relation obtains. The `FieldVal`s for a field might be modified as elaboration
+  proceeds: for example, some might become `.nested`, or some defaults might turn into terms. This
+  all happens during `expandStruct`.
+  The `Struct` holds everything, and is updated throughout the process.
+  One of its fields is `field`, which holds a list of `Field Struct`'s. (The appearance of `Struct`
+  within `Field Struct` is to allow the `Struct`s to nest other `Struct`s when we have subobjects.)
+  The fields of each element of the `field` field (got that?) are
+  * `ref : Syntax`, which holds the `Syntax` found for that field
+  * `lhs : FieldLHS`, which describes the name of the field in question
+  * `val : FieldVal`, which holds the pre-expression `FieldVal`—either `.term stx` where `stx` is
+  the syntax of the field's value, `.default` (now `.missing`) if no syntax was found, or `.nested
+  s` if the field represents a subobject `s` of the structure (e.g. `toFoo`, produced by `extends`)
+  * `expr? : Option Expr`, which holds the elaborated expression when it becomes available (or a
+  metavariable, if the syntax is missing), and which begins at this stage as `none`.
+  `elacStructInstAux` then calls `elabStruct` on the skeletal `Struct` (which has appropriate
+  `FieldVal`s, but `none` for each field's `expr?`), which turns the `Struct` into an
+  `ElabStructResult`.
+  `elabStruct` elaborates everything but defaults, constructing the structure instance as an
+  expression given by the application of the structure's constructor to the values it finds by
+  elaborating the `stx` in any `.term stx` `FieldVal` while ensuring the appropriate type. (It's
+  not quite true that no defaults are taken care of here: `autoparam`s are turned into `.term`s.)
+  If the `FieldVal` is `.nested s`, it calls `elabStruct` on `s`; if it finds a `.default` (now
+  renamed to `.missing`) `FieldVal`, it uses a fresh metavariable in place of an elaborated
+  expression. As it does this, it stores any elaborated expressions in the `expr?` field of its
+  fields and builds this constructor application expression, which is, in the resulting
+  `ElabStructResult` structure, confusingly also named "val". Occasionally the `FieldVals` for each
+  field are updated as well. Also returned in `ElabStructResult` is the updated Struct with all its
+  new fields, and `instMVars`, an array of metavariables for dealing with typeclass instance
+  synthesis.
+  During `elabStruct`, defaults were inserted as metavariables into the constructed expression and
+  into `expr?`, but they were also annotated with ``structInstDefault` to indicate that they
+  represented a missing default value, and needed to be synthesized during the default loop.
+  Indeed, the function `isMissingDefault?` checks that this metavariable is unassigned when
+  deciding whether to return true or false. We finish our elaboration of the structure instance
+  with the `propagate` loop, which iteratively synthesizes the defaults, as sometimes the default
+  values of fields reference other fields which may also have a default value (etc.).
+  # Modifications
+  Changes from `StructInst.lean` are no longer marked with `!!` in a comment (or with `!!/`, `!!\`
+  surrounding a new or altered block). These are however visible in past commits.
+  Existing comments are left unchanged, and new comments begin with "~~".
+  ## Syntax
+  We use the parser from `Term.lean`, but change `optional ".."` to our parseer for variadic holes,
+  `variadicHole`
+  ## Logic
+  The original implementation of `..`, which creates a natural metavariable for each goal (and does
+  not synthesize defaults) affects things early on, at the stage of `FieldVal`s. Instead of using a
+  `.default` `FieldVal`, it makes a hole via syntax by providing a `.term (mkHole ref)` `FieldVal`
+  for each missing field value.
+  We preserve this behavior only for the `isSynthetic := false, useDefaults := false` case.
+  Otherwise, we use the `.default` `FieldVal`—now renamed to `.missing` to reflect its changed
+  function—and intervene mostly within the `ImplicitFields` namespace (previously the
+  `DefaultFields` namespace), where defaults are synthesized. If the variadic hole syntax says not
+  to, we don't propagate the default-synthesizing loop and therefore don't synthesize any defaults.
+  Typically, when the default loop ends with some fields still annotated as missing, an error is
+  thrown (`fields missing: ...`). However, if there's a variadic hole, we simply return from the
+  loop without error; next (whether the loop has run or not) we assign those remaining annotated
+  fields to *new* metavariables, which, in the `isSynthetic := true` case, are well-named and hold
+  all of the metadata we want them to. These are ripe to be used in a `refine` statement.
+  The only exception to this flow is how we handle `autoparam`s: autoparams are handled in
+  `elabStruct`, so that's where we intervene as well.
+  ## Style
+  New code is often written in a "lookahead" fashion, to make it as easy as possible to move this
+  to core, in case it would better belong there. Therefore some cases that don't occur in this
+  elaboration are nonetheless accounted for—for example, the case where variadic hole syntax is
+  absent (where the value of struct.source.implicit is none), and the case where `isSynthetic :=
+  false, useDefaults := false`, which is already accounted for by existing `..` syntax. We use a
+  different token (`...`) only to show that this works.
+  This modification of `StructInst.lean` also attempts to be "minimally invasive" by intervening in
+  as few places as possible and leaving the existing flow of computation intact.
+  ## Locations of changes
+  The changes to existing definitions are localized to the following:
+  ### Necessary parsing and syntax processing changes
+  * The `structInst` term parser was modified to allow variadic hole syntax.
+  * `expandStructInstFieldAbbrev`
+    * update `$[..%$ell]?` syntax match to accommodate variadic holes
+  * type of `implicit` in `Source` structure: `Option Syntax` ⇒ `Option VariadicHoleConfig`
+    * originally this held the syntax `..` if present; now it holds information derived from the
+    variadic hole syntax (if present) as opposed to the raw syntax
+  * `getStructSource`
+    * inserted `getVariadicHoleConfig?` in front of the raw `implicitSource` syntax to process it
+    into a `VariadicHoleConfig`
+  * `formatStruct`
+    * instead of using a literal `".."` whenever `implicit.isSome`, use the syntax we encountered
+    (stored as one of the fields of `VariadicHoleConfig`)
+  ### Logic
+  **Simple renamings**
+  * The `.default` `FieldVal`, which was used to indicate that fields would be synthesized by the
+  default loop, is renamed to `.missing` for clarity. Likewise `Struct.allDefault` is renamed to
+  `Struct.allMissing` (since it simply checks these `FieldVal`s), and `formatField` formats
+  `.missing` fields via `"<missing>"` instead of via `"<default>"`.
+  * We rename the `DefaultFields` namespace to `ImplicitFields`, since this is now where we
+  intervene to handle holes as well.
+  **Setup changes**
+  * `addMissingFields`, which is responsible for attaching `.missing` to unspecified fields,
+  previously attached a `.term (mkHole stx)` to any missing field whenever `..` was present. Here,
+  we only do so in the `isSynthetic := false, useDefaults := false` case, attaching `.missing` in
+  all other cases (both when we exepct them to be synthesized as defaults and not).
+  * `elabStruct` – this function uses `FieldVal`s to 1) generate `expr?`s for each field when
+  possible and 2) apply the structure's constructor to the arguments it finds to build the instance
+  expression. It stops short of synthesizing defaults, inserting a metavariable in both places when
+  it encounters a `.missing` field. However, autoparams for `.missing` values are handled here. We
+  therefore modify that section of the code so that
+    * if the variadic hole says to use holes instead of defaults, we don't try the autoparam
+    * if it says to use defaults, we try the autoparam in such a way that if it fails we use a hole
+    instead
+      * we also need to introduce a new optional `Bool` argument to the internal `cont` function
+      that, when modified from its default, takes a different branch. Otherwise `cont` is
+      untouched, and the original behavior is used when this argument is not specified.
+    * if there's no variadic hole, use the original behavior
+  **Default loop changes**
+  * `propagateLoop` – this is a pass of the loop used for synthesizing defaults, and is responsible
+  for throwing an error when too few fields are specified. If there is a variadic hole, it does not
+  throw that error and simply returns.
+  * `propagate` – this sets things up for the loop and executes it.
+    * We check the variadic hole config and don't run `propagateLoop` if it says not to. (We start
+    with a `do` to accommodate this.)
+    * At the end, if there is a variadic hole, we run `assignRemainingDefaultsToFieldHoles` (a new
+    function which does what you expect)
+  ## New Code
+  The new functionality is in the `ImplicitFields` section to attach metadata to the goals
+  produced. Currently, we attach the metadata as a `KVMap` to the type of the goal, but this may
+  change. We use this metadata to resolve name conflicts, appending an appropriate index if any
+  existing metavariable is from a structure that shares a field name. This is meant to improve
+  clarity: for example, if `Foo` and `Bar` both have fields `x` and `y`,
+  `refine ({ y := 0, ?.. : Foo}, { x := 1, ?.. : Bar})` will produce goals `x` and `y_1` to show
+  that these are not from the same structure. (This may change if we decide to prefix each goal
+  name with the name of the structure.)
+  # Questions
+  * Should `trySynthStructInstance?` be run even when `useDefaults` is `false`?
+  * what about `bi == .instImplicit`? Should default synthesis be avoided in that case too?
+  * Dhould metadata be on the type, or somewhere else?
+  * Is the best way to get a unique id for a syntax instance via getPos? Do we need to do so anyway?
+  * Should utility-like functions be refactored into other files?
+  * Can the docstrings of the original structure instance and `refine` be modified from "within
+    mathlib" somehow?
+  * Do I need to add to "authors" at the top or worry about the copyright?
+  * Check for unreachable code after design decisions have been made.
+-/
+namespace Lean.Elab.Term.StructInstWithHoles
+
+open Meta
+open TSyntax.Compat
+
+/--
+  A synthetic variadic hole. When used in structure instance syntax, it fills the unspecified
+  fields with metavariables named by the field. It synthesizes defaults when possible.
+  It can be followed by an identifier to specify a prefix for the names of the holes.
+ -/
+def vH?dd        := leading_parser "?.." >> Parser.optional Parser.ident
+/--
+  A synthetic variadic hole that does not synthesize any defaults. When used in structure instance
+  syntax, it fills the unspecified fields with metavariables named by the field. It synthesizes
+  defaults when possible. It can be followed by an identifier to specify a prefix for the names of
+  the holes.
+ -/
+def vH?dd!       := leading_parser "?..!" >> Parser.optional Parser.ident
+/-~~! Removed for now.
+/-- A natural variadic hole that does not synthesize defaults. -/
+def vHdd!        := leading_parser "..!"
+/-- A natural variadic hole that synthesizes defaults when possible. -/
+def vHdd         := leading_parser "..."
+-/
+/-- A variadic hole that fills multiple spots with holes.  -/
+def variadicHole := leading_parser (vH?dd <|> vH?dd! /-~~! <|> vHdd! <|> vHdd-/)
+
+open Lean.Parser Lean.Parser.Term in
+/--
+Structure instance. `{ x := e, ... }` assigns `e` to field `x`, which may be
+inherited. If `e` is itself a variable called `x`, it can be elided:
+`fun x => { x , y := 1 }`.
+A *structure update* of an existing value can be given via `with`:
+`{ point with x := 1 }`.
+The structure type can be specified if not inferable:
+`{ x := 1, y := 2 : Point }`.
+`..` can be used in pattern-matching to fill all unspecified fields with `_`:
+`match s with | { x := 1, .. } => ...`
+`?..` fills all unspecified fields with automatically-named goals:
+if a `Foo` has fields `x`, `y`, `z`, `{ x := 1, ?.. } : Foo` creates `?y`, `?z`.
+-/
+@[term_parser] def structInstWithHoles := leading_parser "{" >> ppHardSpace >> Lean.Parser.optional
+(atomic (sepBy1 termParser ", " >> " with "))
+  >> sepByIndent (structInstFieldAbbrev <|> structInstField) ", " (allowTrailingSep := true)
+  >> variadicHole -- Only apply this elaboration to syntax that has one of these holes
+  >> Lean.Parser.optional (" : " >> termParser) >> " }"
+
+/--
+  Syntactically move any type specification outside of the structure instance syntax:
+  `{ x := 0 : Foo }` becomes `{ x := 0 } : Foo`.
+-/
+@[macro structInstWithHoles] def expandStructInstWithHolesExpectedType : Macro := fun stx =>
+  let expectedArg := stx[4]
+  if expectedArg.isNone then
+    Macro.throwUnsupported
+  else
+    let expected := expectedArg[1]
+    let stxNew   := stx.setArg 4 mkNullNode
+    `(($stxNew : $expected))
+
+/-- Expand field abbreviations. Example: `{ x, y := 0 }` expands to `{ x := x, y := 0 }` -/
+@[macro structInstWithHoles] def expandStructInstWithHolesFieldAbbrev : Macro
+  | `({ $[$srcs,* with]? $fields,* $ell:variadicHole $[: $ty]? }) =>
+    if fields.getElems.raw.any (·.getKind == ``Lean.Parser.Term.structInstFieldAbbrev) then do
+      let fieldsNew ← fields.getElems.mapM fun
+        | `(Parser.Term.structInstFieldAbbrev| $id:ident) =>
+          `(Parser.Term.structInstField| $id:ident := $id:ident)
+        | field => return field
+      `({ $[$srcs,* with]? $fieldsNew,* $ell $[: $ty]? })
+    else
+      Macro.throwUnsupported
+  | _ => Macro.throwUnsupported
+
+/--
+  If `stx` is of the form `{ s₁, ..., sₙ with ... }` and `sᵢ` is not a local variable, expand into
+  `let src := sᵢ; { ..., src, ... with ... }`.
+  Note that this one is not a `Macro` because we need to access the local context.
+-/
+private def expandNonAtomicExplicitSources (stx : Syntax) : TermElabM (Option Syntax) := do
+  let sourcesOpt := stx[1]
+  if sourcesOpt.isNone then
+    return none
+  else
+    let sources := sourcesOpt[0]
+    if sources.isMissing then
+      throwAbortTerm
+    let sources := sources.getSepArgs
+    if (← sources.allM fun source => return (← isLocalIdent? source).isSome) then
+      return none
+    if sources.any (·.isMissing) then
+      throwAbortTerm
+    return some (← go sources.toList #[])
+where
+  go (sources : List Syntax) (sourcesNew : Array Syntax) : TermElabM Syntax := do
+    match sources with
+    | [] =>
+      let sources := Syntax.mkSep sourcesNew (mkAtomFrom stx ", ")
+      return stx.setArg 1 (stx[1].setArg 0 sources)
+    | source :: sources =>
+      if (← isLocalIdent? source).isSome then
+        go sources (sourcesNew.push source)
+      else
+        withFreshMacroScope do
+          let sourceNew ← `(src)
+          let r ← go sources (sourcesNew.push sourceNew)
+          `(let src := $source; $r)
+
+/-- Information for any explicit sources encountered (i.e. some `sᵢ` in `s₁, ..., sₙ with`) -/
+structure ExplicitSourceInfo where
+  /-- The syntax of some `sᵢ` in `s₁, ..., sₙ with` -/
+  stx        : Syntax
+  /-- The name of some structure `sᵢ` in `s₁, ..., sₙ with` -/
+  structName : Name
+  deriving Inhabited
+
+/--
+  Information deduced from variadic hole syntax, as well as the raw
+  syntax itself and any identifiers that were found.
+-/
+structure VariadicHoleConfig where
+  /-- The raw variadic hole syntax encountered (`?..`, `..`, etc.)-/
+  stx         : TSyntax ``variadicHole
+  /-- An optional name `x` found in `?..x` or `?..!x`, to be used as a prefix. -/
+  name        : Option Name := none
+  /-- Whether the holes should be synthetic and automatically named. -/
+  isSynthetic : Bool
+  /-- Whether defaults should attempt to be synthesized before filling fields with holes. -/
+  useDefaults : Bool
+  deriving Inhabited, Repr
+
+/--
+  Information on other sources of field values via structure update syntax or variadic holes.
+  Collects of explicit source info (preceding `with` in structure updates) and implicit source
+  info (for specification of holes, e.g. `..` or `?..`).
+-/
+structure Source where
+  /-- info for all `sᵢ` in `s₁, ..., sₙ with` -/
+  explicit : Array ExplicitSourceInfo
+  /-- info for any variadic hole syntax encountered (`?..`, `..`, etc.) -/
+  implicit : Option VariadicHoleConfig
+  deriving Inhabited
+
+/-- Check if neither an explicit nor an implicit source has been specified. -/
+def Source.isNone : Source → Bool
+  | { explicit := #[], implicit := none } => true
+  | _ => false
+
+/-- Process variadic hole syntax into a VariadicHoleConfig. -/
+def getVariadicHoleConfig? : TSyntax ``variadicHole → Option VariadicHoleConfig
+| stx => match stx with
+  | `(variadicHole|?..$[$x:ident]?) => some
+    {stx, isSynthetic := true, useDefaults := true, name := x.map Syntax.getId}
+  | `(variadicHole|?..!$[$x:ident]?) => some
+    {stx, isSynthetic := true, useDefaults := false, name := x.map Syntax.getId}
+  | _ => none
+
+/--
+  Put an array of source syntax into a form which matches
+  `optional (atomic (sepBy1 termParser ", " >> " with ")`, e.g. `s₁, s₂, s₃ with`.
+  Should only be called when `sources` is a nonempty `Array`.
+  -/
+private def mkSourcesWithSyntax (sources : Array Syntax) : Syntax :=
+  let ref := sources[0]!
+  let stx := Syntax.mkSep sources (mkAtomFrom ref ", ")
+  mkNullNode #[stx, mkAtomFrom ref "with "]
+
+/--
+  Extract and process both explicit (`s₁, ..., sₙ with`) and implicit (`..`, `?..`, etc.) source
+  syntax from structure syntax.
+-/
+private def getStructSource (structStx : Syntax) : TermElabM Source :=
+  withRef structStx do
+    let explicitSource := structStx[1]
+    let implicitSource := structStx[3]
+    let explicit ← if explicitSource.isNone then
+      pure #[]
+    else
+      explicitSource[0].getSepArgs.mapM fun stx => do
+        let some src ← isLocalIdent? stx | unreachable!
+        addTermInfo' stx src
+        let srcType ← whnf (← inferType src)
+        tryPostponeIfMVar srcType
+        let structName ← getStructureName srcType
+        return { stx, structName }
+    let implicit :=
+      if implicitSource[0].isNone
+      then none
+      else getVariadicHoleConfig? implicitSource
+    return { explicit, implicit }
+
+/--
+  We say a `{ ... }` notation is a `modifyOp` if it contains only one
+  ```
+  def structInstArrayRef := leading_parser "[" >> termParser >>"]"
+  ```
+-/
+private def isModifyOp? (stx : Syntax) : TermElabM (Option Syntax) := do
+  let s? ← stx[2].getSepArgs.foldlM (init := none) fun s? arg => do
+    /- arg is of the form `structInstFieldAbbrev <|> structInstField` -/
+    if arg.getKind == ``Lean.Parser.Term.structInstField then
+      /- Remark: the syntax for `structInstField` is
+         ```
+         def structInstLVal   := leading_parser (ident <|> numLit <|> structInstArrayRef) >> many
+         (group ("." >> (ident <|> numLit)) <|> structInstArrayRef)
+         def structInstField  := leading_parser structInstLVal >> " := " >> termParser
+         ```
+      -/
+      let lval := arg[0]
+      let k    := lval[0].getKind
+      if k == ``Lean.Parser.Term.structInstArrayRef then
+        match s? with
+        | none   => return some arg
+        | some s =>
+          if s.getKind == ``Lean.Parser.Term.structInstArrayRef then
+            throwErrorAt arg "invalid \{...} notation, at most one `[..]` at a given level"
+          else
+            throwErrorAt arg "invalid \{...} notation, can't mix field and `[..]` at a given level"
+      else
+        match s? with
+        | none   => return some arg
+        | some s =>
+          if s.getKind == ``Lean.Parser.Term.structInstArrayRef then
+            throwErrorAt arg "invalid \{...} notation, can't mix field and `[..]` at a given level"
+          else
+            return s?
+    else
+      return s?
+  match s? with
+  | none   => return none
+  | some s => if s[0][0].getKind == ``Lean.Parser.Term.structInstArrayRef then return s? else
+  return none
+
+/-- Elaborate `modifyOp`s given a single explicit source. -/
+private def elabModifyOp (stx modifyOp : Syntax) (sources : Array ExplicitSourceInfo)
+(expectedType? : Option Expr) : TermElabM Expr := do
+  if sources.size > 1 then
+    throwError "invalid \{...} notation, multiple sources and array update is not supported."
+  let cont (val : Syntax) : TermElabM Expr := do
+    let lval := modifyOp[0][0]
+    let idx  := lval[1]
+    let self := sources[0]!.stx
+    let stxNew ← `($(self).modifyOp (idx := $idx) (fun s => $val))
+    trace[Elab.struct.modifyOp] "{stx}\n===>\n{stxNew}"
+    withMacroExpansion stx stxNew <| elabTerm stxNew expectedType?
+  let rest := modifyOp[0][1]
+  if rest.isNone then
+    cont modifyOp[2]
+  else
+    let s ← `(s)
+    let valFirst  := rest[0]
+    let valFirst  := if valFirst.getKind == ``Lean.Parser.Term.structInstArrayRef then valFirst
+      else valFirst[1]
+    let restArgs  := rest.getArgs
+    let valRest   := mkNullNode restArgs[1:restArgs.size]
+    let valField  := modifyOp.setArg 0 <| mkNode ``Parser.Term.structInstLVal #[valFirst, valRest]
+    let valSource := mkSourcesWithSyntax #[s]
+    let val       := stx.setArg 1 valSource
+    let val       := val.setArg 2 <| mkNullNode #[valField]
+    trace[Elab.struct.modifyOp] "{stx}\nval: {val}"
+    cont val
+
+/--
+  Get structure name.
+  This method tries to postpone execution if the expected type is not available.
+  If the expected type is available and it is a structure, then we use it.
+  Otherwise, we use the type of the first source.
+-/
+private def getStructName (expectedType? : Option Expr) (sourceView : Source) : TermElabM Name := do
+  tryPostponeIfNoneOrMVar expectedType?
+  let useSource : Unit → TermElabM Name := fun _ => do
+    unless sourceView.explicit.isEmpty do
+      return sourceView.explicit[0]!.structName
+    match expectedType? with
+    | some expectedType => throwUnexpectedExpectedType expectedType
+    | none => throwUnknownExpectedType
+  match expectedType? with
+  | none => useSource ()
+  | some expectedType =>
+    let expectedType ← whnf expectedType
+    match expectedType.getAppFn with
+    | Expr.const constName _ =>
+      unless isStructure (← getEnv) constName do
+        throwError "invalid \{...} notation, structure type expected{indentExpr expectedType}"
+      return constName
+    | _                      => useSource ()
+where
+  throwUnknownExpectedType :=
+    throwError "invalid \{...} notation, expected type is not known"
+  throwUnexpectedExpectedType type (kind := "expected") := do
+    let type ← instantiateMVars type
+    if type.getAppFn.isMVar then
+      throwUnknownExpectedType
+    else
+      throwError "invalid \{...} notation, {kind} type is not of the form (C ...){indentExpr type}"
+
+/-- Information on the left hand side of a binding encountered in structure syntax. -/
+inductive FieldLHS where
+  /-- A representation of the name of a field as encountered in binding syntax (e.g. `x` in
+      `x := ...`). -/
+  | fieldName  (ref : Syntax) (name : Name)
+  /-- A representation of the index of a field as encountered in binding syntax (e.g. `3` in
+      `3 := ...`). -/
+  | fieldIndex (ref : Syntax) (idx : Nat)
+  /-- A representation of a modifyOp as encountered in binding syntax. -/
+  | modifyOp   (ref : Syntax) (index : Syntax)
+  deriving Inhabited
+
+instance : ToFormat FieldLHS := ⟨fun lhs =>
+  match lhs with
+  | .fieldName _ n  => format n
+  | .fieldIndex _ i => format i
+  | .modifyOp _ i   => "[" ++ i.prettyPrint ++ "]"⟩
+
+/--
+  A limited, pre-expression description of the values of fields. Only terms given by raw syntax,
+  nested values (for subobjects), and missing values are can be specified.
+  The polymorphism via its `Type` argument is only used for nested `FieldVal`s, which need to
+  know what type their argument should be. In practice, we only ever take this argument to be
+  `Struct`.
+  -/
+inductive FieldVal (σ : Type) where
+  /-- Term syntax encountered on the RHS of a binding, e.g. `1+1` in `x := 1+1`. -/
+  | term  (stx : Syntax) : FieldVal σ
+  /-- A nested `FieldVal`, which in practice is used to hold subobjects as `Struct`s. -/
+  | nested (s : σ)       : FieldVal σ
+  /-- An indication that this field was missing, i.e. not specified explicitly in the syntax. -/
+  | missing              : FieldVal σ
+  deriving Inhabited
+
+/--
+  A representation of a field in a structure. This contains the original syntax of the field
+  (`ref`), a representation of the LHS of the `:=` binding (`lhs`), the pre-expression `FieldVal`
+  (`val`), and the actual expression that we take to be the value of the field (`expr?`).
+  `expr?` begins as `none`, and is modified over the course of this code as we figure out whether
+  we need to elaborate some syntax encountered (e.g. if `.term stx` is in `val`) or if the field
+  value is `.missing` (in which case we make a metavariable).
+-/
+structure Field (σ : Type) where
+  /-- The syntax of the binding used to specify this field. -/
+  ref   : Syntax
+  /-- Information on the LHS of the binding used to specify this field. -/
+  lhs   : List FieldLHS
+  /-- The basic content of the field value, prior to elaboration. -/
+  val   : FieldVal σ
+  /-- The elaborated value of the field in question as it becomes available, which starts
+      out as `none` and is updated during `elabStruct` with either elaborated terms or
+      metavariables which may get assigned to synthesized defaults. -/
+  expr? : Option Expr := none
+  deriving Inhabited
+
+/-- Check if the LHS of the binding specifying a field is a single `FieldLHS`. -/
+def Field.isSimple {σ} : Field σ → Bool
+  | { lhs := [_], .. } => true
+  | _                  => false
+
+/--
+  The organized content of the structure instance.
+  The field `params` is used for `.missing` value propagation. It is initially empty, and
+  then set at `elabStruct`. -/
+inductive Struct where
+  | mk (ref : Syntax) (structName : Name) (params : Array (Name × Expr))
+  (fields : List (Field Struct)) (source : Source)
+  deriving Inhabited
+
+/-- Abbreviation for `List (Field Struct)`: A list of representations of the structure's fields. -/
+abbrev Fields := List (Field Struct)
+
+/-- The original syntax of the structure instance. -/
+def Struct.ref : Struct → Syntax
+  | ⟨ref, _, _, _, _⟩ => ref
+
+/-- The name of the structure. -/
+def Struct.structName : Struct → Name
+  | ⟨_, structName, _, _, _⟩ => structName
+
+/-- Parameters used during the initial processing of `.missing` fields. Initially `none`, and set
+    at `elabStruct`. -/
+def Struct.params : Struct → Array (Name × Expr)
+  | ⟨_, _, params, _, _⟩ => params
+
+/-- The list of `fields` in the structure instance as `Field Struct`s. Updated over the course of
+    the elaboration to include computed values. -/
+def Struct.fields : Struct → Fields
+  | ⟨_, _, _, fields, _⟩ => fields
+
+/-- Information on other sources of values for the structure. Namely, any structures preceding
+    `with` in structure update syntax and any variadic holes (`..`, `?..`) following the field
+    bindings. -/
+def Struct.source : Struct → Source
+  | ⟨_, _, _, _, s⟩ => s
+
+/-- `true` iff all fields of the given structure are marked as `.missing`. -/
+partial def Struct.allMissing (s : Struct) : Bool :=
+  s.fields.all fun { val := val,  .. } => match val with
+    | .term _   => false
+    | .missing  => true
+    | .nested s => allMissing s
+
+/-- Pretty-prints a field (`Field Struct`). Uses the field LHS's and its `val : FieldVal Struct`. -/
+def formatField (formatStruct : Struct → Format) (field : Field Struct) : Format :=
+  Format.joinSep field.lhs " . " ++ " := " ++
+    match field.val with
+    | .term v   => v.prettyPrint
+    | .nested s => formatStruct s
+    | .missing  => "<missing>"
+
+/-- Pretty-prints a `Struct`. -/
+partial def formatStruct : Struct → Format
+  | ⟨_, _,          _, fields, source⟩ =>
+    let fieldsFmt := Format.joinSep (fields.map (formatField formatStruct)) ", "
+    let implicitFmt := match source.implicit with
+    | some v => format v.stx
+    | none   => ""
+    if source.explicit.isEmpty then
+      "{" ++ fieldsFmt ++ implicitFmt ++ "}"
+    else
+      "{" ++ format (source.explicit.map (·.stx)) ++ " with " ++ fieldsFmt ++ implicitFmt ++ "}"
+
+instance : ToFormat Struct := ⟨formatStruct⟩
+instance : ToString Struct := ⟨toString ∘ format⟩
+
+instance : ToFormat (Field Struct) := ⟨formatField formatStruct⟩
+instance : ToString (Field Struct) := ⟨toString ∘ format⟩
+
+/--
+Turns a `FieldLHS` into syntax. The first argument specifies whether this is the first in a list of
+`FieldLHS`'s or not.
+Recall that `structInstField` elements have the form
+```
+   def structInstField  := leading_parser structInstLVal >> " := " >> termParser
+   def structInstLVal   := leading_parser (ident <|> numLit <|> structInstArrayRef)
+   >> many (("." >> (ident <|> numLit)) <|> structInstArrayRef)
+   def structInstArrayRef := leading_parser "[" >> termParser >>"]"
+```
+Remark: this code relies on the fact that `expandStruct` only transforms `fieldLHS.fieldName`
+-/
+def FieldLHS.toSyntax (first : Bool) : FieldLHS → Syntax
+  | .modifyOp   stx _    => stx
+  | .fieldName  stx name => if first then mkIdentFrom stx name
+    else mkGroupNode #[mkAtomFrom stx ".", mkIdentFrom stx name]
+  | .fieldIndex stx _    => if first then stx else mkGroupNode #[mkAtomFrom stx ".", stx]
+
+/-- Extracts the `stx` from a `.term stx : FieldVal Struct`. Panics when called on any other
+    constructor of `FieldVal Struct`. -/
+def FieldVal.toSyntax : FieldVal Struct → Syntax
+  | .term stx => stx
+  | _         => unreachable!
+
+/-- Turns a field (as a `Field Struct`) into syntax if has a `val` of the form `.term stx`; panics
+    otherwise. Panics if the `lhs` is an empty list. -/
+def Field.toSyntax : Field Struct → Syntax
+  | field =>
+    let stx := field.ref
+    let stx := stx.setArg 2 field.val.toSyntax
+    match field.lhs with
+    | first::rest => stx.setArg 0 <| mkNullNode
+      #[first.toSyntax true, mkNullNode <| rest.toArray.map (FieldLHS.toSyntax false) ]
+    | _ => unreachable!
+
+/-- Processes syntax into a `FieldLHS`. -/
+private def toFieldLHS (stx : Syntax) : MacroM FieldLHS :=
+  if stx.getKind == ``Lean.Parser.Term.structInstArrayRef then
+    return FieldLHS.modifyOp stx stx[1]
+  else
+    -- Note that the representation of the first field is different.
+    let stx := if stx.getKind == groupKind then stx[1] else stx
+    if stx.isIdent then
+      return FieldLHS.fieldName stx stx.getId.eraseMacroScopes
+    else match stx.isFieldIdx? with
+      | some idx => return FieldLHS.fieldIndex stx idx
+      | none     => Macro.throwError "unexpected structure syntax"
+
+/-- Processes structure instance syntax into a `Struct` given the `structName` and its `source`s. -/
+private def mkStructView (stx : Syntax) (structName : Name) (source : Source) : MacroM Struct := do
+  /- Recall that `stx` is of the form
+     ```
+     leading_parser "{" >> optional (atomic (sepBy1 termParser ", " >> " with "))
+                 >> sepByIndent (structInstFieldAbbrev <|> structInstField) ...
+                 >> variadicHole
+                 >> optional (" : " >> termParser)
+                 >> " }"
+     ```
+     This method assumes that `structInstFieldAbbrev` had already been expanded.
+  -/
+  let fields ← stx[2].getSepArgs.toList.mapM fun fieldStx => do
+    let val      := fieldStx[2]
+    let first    ← toFieldLHS fieldStx[0][0]
+    let rest     ← fieldStx[0][1].getArgs.toList.mapM toFieldLHS
+    return { ref := fieldStx, lhs := first :: rest, val := FieldVal.term val : Field Struct }
+  return ⟨stx, structName, #[], fields, source⟩
+
+/-- (Monadic) Modifies a `Struct`'s fields with a monadic function. -/
+def Struct.modifyFieldsM {m : Type → Type} [Monad m] (s : Struct) (f : Fields → m Fields) :
+m Struct :=
+  match s with
+  | ⟨ref, structName, params, fields, source⟩ =>
+    return ⟨ref, structName, params, (← f fields), source⟩
+
+/-- Modify a `Struct`'s `Fields` with a function. -/
+def Struct.modifyFields (s : Struct) (f : Fields → Fields) : Struct :=
+  Id.run <| s.modifyFieldsM f
+
+/-- Overwrite a `Struct`'s fields. -/
+def Struct.setFields (s : Struct) (fields : Fields) : Struct :=
+  s.modifyFields fun _ => fields
+
+/-- Overwrite a `Struct`'s params. -/
+def Struct.setParams (s : Struct) (ps : Array (Name × Expr)) : Struct :=
+  match s with
+  | ⟨ref, structName, _, fields, source⟩ => ⟨ref, structName, ps, fields, source⟩
+
+/-- Breaks down non-anonymous names in the lhs of fields into lists of their components.  -/
+private def expandCompositeFields (s : Struct) : Struct :=
+  s.modifyFields fun fields => fields.map fun field => match field with
+    | { lhs := .fieldName _ (.str Name.anonymous ..) :: _, .. } => field
+    | { lhs := .fieldName ref n@(.str ..) :: rest, .. } =>
+      let newEntries := n.components.map <| FieldLHS.fieldName ref
+      { field with lhs := newEntries ++ rest }
+    | _ => field
+
+/-- Replaces field lhs's that are specified by index with the name of the field (as registered in
+    the structure). -/
+private def expandNumLitFields (s : Struct) : TermElabM Struct :=
+  s.modifyFieldsM fun fields => do
+    let env ← getEnv
+    let fieldNames := getStructureFields env s.structName
+    fields.mapM fun field => match field with
+      | { lhs := .fieldIndex ref idx :: rest, .. } =>
+        if idx == 0 then throwErrorAt ref "invalid field index, index must be greater than 0"
+        else if idx > fieldNames.size
+          then throwErrorAt ref "invalid field index, structure has only #{fieldNames.size} fields"
+        else return { field with lhs := .fieldName ref fieldNames[idx - 1]! :: rest }
+      | _ => return field
+
+/-- For example, consider the following structures:
+   ```
+   structure A where
+     x : Nat
+   structure B extends A where
+     y : Nat
+   structure C extends B where
+     z : Bool
+   ```
+   This method expands parent structure fields using the path to the parent structure.
+   For example,
+   ```
+   { x := 0, y := 0, z := true : C }
+   ```
+   is expanded into
+   ```
+   { toB.toA.x := 0, toB.y := 0, z := true : C }
+   ```
+-/
+private def expandParentFields (s : Struct) : TermElabM Struct := do
+  let env ← getEnv
+  s.modifyFieldsM fun fields => fields.mapM fun field => do match field with
+    | { lhs := .fieldName ref fieldName :: _,    .. } =>
+      addCompletionInfo <| CompletionInfo.fieldId ref fieldName (← getLCtx) s.structName
+      match findField? env s.structName fieldName with
+      | none => throwErrorAt ref "'{fieldName}' is not a field of structure '{s.structName}'"
+      | some baseStructName =>
+        if baseStructName == s.structName then pure field
+        else match getPathToBaseStructure? env baseStructName s.structName with
+          | some path =>
+            let path := path.map fun funName => match funName with
+              | .str _ s => .fieldName ref (Name.mkSimple s)
+              | _        => unreachable!
+            return { field with lhs := path ++ field.lhs }
+          | _ => throwErrorAt ref "failed to access field '{fieldName}' in parent structure"
+    | _ => return field
+
+/-- Abbreviation for `HashMap Name Fields`: A hash map from field names to lists of representations
+    of fields. -/
+private abbrev FieldMap := HashMap Name Fields
+
+/-- Creates a hash map from field names to lists of representations of fields. The length of the
+    list can be greater than one if the field is not simple. Panics if the lhs of a field is empty.
+    -/
+private def mkFieldMap (fields : Fields) : TermElabM FieldMap :=
+  fields.foldlM (init := {}) fun fieldMap field =>
+    match field.lhs with
+    | .fieldName _ fieldName :: _    =>
+      match fieldMap.find? fieldName with
+      | some (prevField::restFields) =>
+        if field.isSimple || prevField.isSimple then
+          throwErrorAt field.ref "field '{fieldName}' has already been specified"
+        else
+          return fieldMap.insert fieldName (field::prevField::restFields)
+      | _ => return fieldMap.insert fieldName [field]
+    | _ => unreachable!
+
+/-- Unwraps a `Field Struct` from a list of length one, and otherwise returns `none`. -/
+private def isSimpleField? : Fields → Option (Field Struct)
+  | [field] => if field.isSimple then some field else none
+  | _       => none
+
+/-- Finds the index of the field name in its third argument in the list of field names in its
+    second. The first argument, the name of the structure, is used only for descriptive error
+    messages. -/
+private def getFieldIdx (structName : Name) (fieldNames : Array Name) (fieldName : Name) :
+TermElabM Nat := do
+  match fieldNames.findIdx? fun n => n == fieldName with
+  | some idx => return idx
+  | none     => throwError "field '{fieldName}' is not a valid field of '{structName}'"
+
+/-- Constructs the syntax for a field projection. Only does so if the given field name is in fact a
+    field of the given structure name; returns `none` otherwise. -/
+def mkProjStx? (s : Syntax) (structName : Name) (fieldName : Name) : TermElabM (Option Syntax) := do
+  if (findField? (← getEnv) structName fieldName).isNone then
+    return none
+  return some <| mkNode ``Parser.Term.proj #[s, mkAtomFrom s ".", mkIdentFrom s fieldName]
+
+/-- Gets a field from a list of fields by name. If not found, returns `none`. -/
+def findField? (fields : Fields) (fieldName : Name) : Option (Field Struct) :=
+  fields.find? fun field =>
+    match field.lhs with
+    | [.fieldName _ n] => n == fieldName
+    | _                => false
+
+mutual
+
+  /-- Group fields that belong to a subobject as a `Struct` under that subobject field via a
+      `.nested s` `FieldVal`. For example, a `Struct` representing
+      `{ toFoo.x := 1, toFoo.y := 2, z := 3 }` will become one representing
+      `{ toFoo := { x := 1, y := 2 }, z := 3 }`.
+  -/
+  private partial def groupFields (s : Struct) : TermElabM Struct := do
+    let env ← getEnv
+    withRef s.ref do
+    s.modifyFieldsM fun fields => do
+      let fieldMap ← mkFieldMap fields
+      fieldMap.toList.mapM fun ⟨fieldName, fields⟩ => do
+        match isSimpleField? fields with
+        | some field => pure field
+        | none =>
+          let substructFields := fields.map fun field => { field with lhs := field.lhs.tail! }
+          let field := fields.head!
+          match Lean.isSubobjectField? env s.structName fieldName with
+          | some substructName =>
+            let substruct := Struct.mk s.ref substructName #[] substructFields s.source
+            let substruct ← expandStruct substruct
+            pure { field with lhs := [field.lhs.head!], val := FieldVal.nested substruct }
+          | none =>
+            let updateSource (structStx : Syntax) : TermElabM Syntax := do
+              let sourcesNew ← s.source.explicit.filterMapM
+                fun source => mkProjStx? source.stx source.structName fieldName
+              let explicitSourceStx := if sourcesNew.isEmpty then mkNullNode
+                else mkSourcesWithSyntax sourcesNew
+              let implicitSourceStx := s.source.implicit.map (·.stx) |>.getD mkNullNode
+              return (structStx.setArg 1 explicitSourceStx).setArg 3 implicitSourceStx
+            let valStx := s.ref -- construct substructure syntax using s.ref as template
+            let valStx := valStx.setArg 4 mkNullNode -- erase optional expected type
+            let args   := substructFields.toArray.map (·.toSyntax)
+            let valStx := valStx.setArg 2 (mkNullNode <| mkSepArray args (mkAtom ","))
+            let valStx ← updateSource valStx
+            return { field with lhs := [field.lhs.head!], val := FieldVal.term valStx }
+
+  /--
+    Add `val : FieldVal`s to fields as specified by the sources.
+    If a value is found in the explicit sources (prior to `with`), add it as a `.term` or a
+    `.nested` `FieldVal`, as appropriate. If not, check for `..`, and make a hole via syntax as a
+    `.term`. Otherwise, mark the field as as `.missing`.
+  -/
+  private partial def addMissingFields (s : Struct) : TermElabM Struct := do
+    let env ← getEnv
+    let fieldNames := getStructureFields env s.structName
+    let ref := s.ref.mkSynthetic
+    withRef ref do
+      let fields ← fieldNames.foldlM (init := []) fun fields fieldName => do
+        match findField? s.fields fieldName with
+        | some field => return field::fields
+        | none       =>
+          let addField (val : FieldVal Struct) : TermElabM Fields := do
+            return { ref, lhs := [FieldLHS.fieldName ref fieldName], val := val } :: fields
+          match Lean.isSubobjectField? env s.structName fieldName with
+          | some substructName =>
+            -- If one of the sources has the subobject field, use it
+            if let some val ← s.source.explicit.findSomeM?
+              fun source => mkProjStx? source.stx source.structName fieldName
+            then
+              addField (FieldVal.term val)
+            else
+              let substruct := Struct.mk ref substructName #[] [] s.source
+              let substruct ← expandStruct substruct
+              addField (FieldVal.nested substruct)
+          | none =>
+            if let some val ← s.source.explicit.findSomeM?
+              fun source => mkProjStx? source.stx source.structName fieldName
+            then
+              addField (FieldVal.term val)
+            else
+              -- Use hole syntax as a term in the natural, no-defaults (`..`) case;
+              -- otherwise mark it as a missing field.
+              match s.source.implicit with
+              | some { isSynthetic := false, useDefaults := false, .. } =>
+                addField (FieldVal.term (mkHole ref))
+              | _ => addField FieldVal.missing
+      return s.setFields fields.reverse
+
+  /-- Put the `Struct` into canonical form by expanding different ways of specifying fields
+      (composite, by index, subobject); group fields by subobject; and incorporate values (or
+      holes) sources. -/
+  private partial def expandStruct (s : Struct) : TermElabM Struct := do
+    let s := expandCompositeFields s
+    let s ← expandNumLitFields s
+    let s ← expandParentFields s
+    let s ← groupFields s
+    addMissingFields s
+
+end
+
+/-- Information about the constructor. -/
+structure CtorHeaderResult where
+  /-- The constructor function itself as an `Expr`. -/
+  ctorFn     : Expr
+  /-- The type of the constructor as an `Expr`. -/
+  ctorFnType : Expr
+  /-- Metavariables for instances. -/
+  instMVars  : Array MVarId
+  /-- Named parameters encountered in bindings of the type and the expressions used for them. -/
+  params     : Array (Name × Expr)
+
+/-- Helper function that processes the constructor and its type until its first parameter reaches 0.
+-/
+private def mkCtorHeaderAux :
+Nat → Expr → Expr → Array MVarId → Array (Name × Expr) → TermElabM CtorHeaderResult
+  | 0,   type, ctorFn, instMVars, params =>
+    return { ctorFn , ctorFnType := type, instMVars, params }
+  | n+1, type, ctorFn, instMVars, params => do
+    match (← whnfForall type) with
+    | .forallE paramName d b c =>
+      match c with
+      | .instImplicit =>
+        let a ← mkFreshExprMVar d .synthetic
+        mkCtorHeaderAux n (b.instantiate1 a) (mkApp ctorFn a) (instMVars.push a.mvarId!)
+          (params.push (paramName, a))
+      | _ =>
+        let a ← mkFreshExprMVar d
+        mkCtorHeaderAux n (b.instantiate1 a) (mkApp ctorFn a) instMVars (params.push (paramName, a))
+    | _ => throwError "unexpected constructor type"
+
+/-- Burrows into the body of a `.forallE` expression `n` times if possible, and returns the result.
+    If an expression not of the form `.forallE` is encountered along the way, return `none`.  -/
+private partial def getForallBody : Nat → Expr → Option Expr
+  | i+1, .forallE _ _ b _ => getForallBody i b
+  | _+1, _                => none
+  | 0,   type             => type
+
+/-- When the expected type is known, attempt to get the type of the constructor by stripping `n`
+    `.forallE`'s off of the expression and then assigning metavariables by `isDefEq`'ing with
+    the expected type. -/
+private def propagateExpectedType (type : Expr) (numFields : Nat) (expectedType? : Option Expr) :
+TermElabM Unit := do
+  match expectedType? with
+  | none              => return ()
+  | some expectedType =>
+    match getForallBody numFields type with
+      | none           => pure ()
+      | some typeBody =>
+        unless typeBody.hasLooseBVars do
+          discard <| isDefEq expectedType typeBody
+
+/-- Process information about a given `ConstructorVal`. -/
+private def mkCtorHeader (ctorVal : ConstructorVal) (expectedType? : Option Expr) :
+TermElabM CtorHeaderResult := do
+  let us ← mkFreshLevelMVars ctorVal.levelParams.length
+  let val  := Lean.mkConst ctorVal.name us
+  let type ← instantiateTypeLevelParams (ConstantInfo.ctorInfo ctorVal) us
+  let r ← mkCtorHeaderAux ctorVal.numParams type val #[] #[]
+  propagateExpectedType r.ctorFnType ctorVal.numFields expectedType?
+  synthesizeAppInstMVars r.instMVars r.ctorFn
+  return r
+
+/-- Annotate an expression to indicate that it must be synthesized as a default value.
+    In practice, the expression is a metavariable. -/
+def markDefaultMissing (e : Expr) : Expr :=
+  mkAnnotation `structInstDefault e
+
+/-- Check if an expression has been annotated in a way that indicates it should be synthesized
+    during the default loop. -/
+def defaultMissing? (e : Expr) : Option Expr :=
+  annotation? `structInstDefault e
+
+/-- Provide a descriptive error message if the structure instance elaboration fails. -/
+def throwFailedToElabField {α} (fieldName : Name) (structName : Name) (msgData : MessageData) :
+TermElabM α :=
+  throwError "failed to elaborate field '{fieldName}' of '{structName}, {msgData}"
+
+/-- Attempt to synthesize an -/
+def trySynthStructInstance? (s : Struct) (expectedType : Expr) : TermElabM (Option Expr) := do
+  if !s.allMissing then
+    return none
+  else
+    try synthInstance? expectedType catch _ => return none
+
+-- By Mario Carneiro
+/-- Use an expression in syntax. Example: ``(foo $(← toSyntax e))`.
+    This works by creating syntax for a metavariable, then elaborating that syntax and assigning
+    the metavariable to the expression in question.
+ -/
+def toSyntax (e : Expr) (type? : Option Expr := none) : TermElabM Syntax := withFreshMacroScope do
+  let stx ← `(?a)
+  let mvar ← elabTerm stx type?
+  mvar.mvarId!.assign e
+  pure stx
+
+/--
+  The result of running `elabStruct` on a `Struct`, containing:
+  * `struct : Struct`, now with updated `expr?` values in its fields, representing the values for
+    those fields.
+  * `val : Expr`, the constructor applied to the field values (`expr?`s). This is the actual
+    expression that the structure instance elaborates to. (Note that this is distinct from the
+    `val` of each field, which is a `FieldVal`.)
+  * `instMVars : Array MVarId`, used forkeeping track of instances.
+  -/
+structure ElabStructResult where
+  /-- The structure's constructor applied to the field values (`expr?`s). This is the actual
+      expression that the structure instance elaborates to. -/
+  val       : Expr
+  /-- The `struct` that was fed to `elabStruct`, but now with updated `expr?` values for all of its
+      fields containing their values as expressions. -/
+  struct    : Struct
+  /-- Used for keeping track of instances. -/
+  instMVars : Array MVarId
+
+/--
+  Elaborates a `Struct` into an `ElabStructResult`.
+  This computes expressions for all fields of a structure (in `expr?`) on the basis of `FieldVal`s
+  while simultaneously building the elaboration of the structure instance itself, in the form of
+  its constructor applied to the expressions for each of its fields in turn.
+  `.term stx` `FieldVals` are elaborated while ensuring the type (as given by the constructor's
+  type), `.nested s` `FieldVals` are recursed into. `.missing` `FieldVals` are replaced with
+  metavariables and annotated to indicate that they will get assigned during the default synthesis
+  loop. Note that in this case the same metavariable is used both in the `expr?` field and the
+  final constructed expression (`val`), so that assigning it gives access to the value in both
+  places. The one exception is if an `autoParam` is encountered in the type, in which case the
+  tactic is elaborated.
+-/
+private partial def elabStruct (s : Struct) (expectedType? : Option Expr) :
+TermElabM ElabStructResult := withRef s.ref do
+  let env ← getEnv
+  let vhc? := s.source.implicit
+  let ctorVal := getStructureCtor env s.structName
+  if isPrivateNameFromImportedModule env ctorVal.name then
+    throwError "invalid \{...} notation, constructor for `{s.structName}` is marked as private"
+  -- We store the parameters at the resulting `Struct`.
+  -- We use this information during default value propagation.
+  let { ctorFn, ctorFnType, params, .. } ← mkCtorHeader ctorVal expectedType?
+  let (e, _, fields, instMVars) ← s.fields.foldlM
+    (init := (ctorFn, ctorFnType, [], #[]))
+    fun (e, type, fields, instMVars) field => do
+    match field.lhs with
+    | [.fieldName ref fieldName] =>
+      let type ← whnfForall type
+      trace[Elab.struct] "elabStruct {field}, {type}"
+      match type with
+      | .forallE _ d b bi =>
+        let cont (val : Expr) (field : Field Struct) (instMVars := instMVars)
+        (updateField := true) : TermElabM (Expr × Expr × Fields × Array MVarId) := do
+          pushInfoTree <| InfoTree.node (children := {}) <| Info.ofFieldInfo {
+            projName := s.structName.append fieldName,
+            fieldName,
+            lctx := (← getLCtx),
+            val,
+            stx := ref }
+          let e     := mkApp e val
+          let type  := b.instantiate1 val
+          let field := if updateField then { field with expr? := some val } else field
+          return (e, type, field::fields, instMVars)
+        match field.val with
+        | .term stx =>
+          cont (← elabTermEnsuringType stx d.consumeTypeAnnotations) field
+        | .nested s  =>
+          let inst? := if vhc?.all (·.useDefaults) then
+            (← trySynthStructInstance? s d) else none
+          match inst? with
+          | some val =>
+            cont val { field with val := FieldVal.term (mkHole field.ref) }
+          | none     =>
+            let { val, struct := sNew, instMVars := instMVarsNew } ← elabStruct s (some d)
+            let val ← ensureHasType d val
+            cont val { field with val := FieldVal.nested sNew } (instMVars ++ instMVarsNew)
+        | .missing  =>
+          match d.getAutoParamTactic? with
+          | some (.const tacticDecl ..) =>
+            let d := (d.getArg! 0).consumeTypeAnnotations
+            if vhc?.all (·.useDefaults) then
+              match evalSyntaxConstant env (← getOptions) tacticDecl with
+              | .error err       => throwError err
+              | .ok tacticSyntax =>
+                if vhc?.isSome then
+                  let val := (← mkFreshExprMVar (some d) .synthetic)
+                  let stx ← `(by first | $tacticSyntax | exact $(← toSyntax val))
+                  cont (← elabTermEnsuringType stx d)
+                    {field with expr? := some (markDefaultMissing val)}
+                    (updateField := false)
+                else
+                  let stx ← `(by $tacticSyntax)
+                  cont (← elabTermEnsuringType stx d) field
+            else
+              let val ← withRef field.ref <| mkFreshExprMVar (some d)
+              cont (markDefaultMissing val) field
+          | _ =>
+            if bi == .instImplicit then
+              let val ← withRef field.ref <| mkFreshExprMVar d .synthetic
+              trace[Elab.struct] ".instImplicit ({val})"
+              cont val field (instMVars.push val.mvarId!)
+            else
+              let val ← withRef field.ref <| mkFreshExprMVar (some d)
+              cont (markDefaultMissing val) field
+      | _ => withRef field.ref (throwFailedToElabField
+          fieldName s.structName m!"unexpected constructor type{indentExpr type}")
+    | _ => throwErrorAt field.ref "unexpected unexpanded structure field"
+  return { val := e, struct := s.setFields fields.reverse |>.setParams params, instMVars }
+
+namespace ImplicitFields
+
+/-- Updated as we search for default values. We must search for default values overriden in derived
+    structures. -/
+structure Context where
+  /-- `Struct`s in the context which might supply default values. -/
+  structs : Array Struct := #[]
+  /-- The names of structures in the context which might supply default values. -/
+  allStructNames : Array Name := #[]
+  /--
+  Consider the following example:
+  ```
+  structure A where
+    x : Nat := 1
+  structure B extends A where
+    y : Nat := x + 1
+    x := y + 1
+  structure C extends B where
+    z : Nat := 2*y
+    x := z + 3
+  ```
+  And we are trying to elaborate a structure instance for `C`.
+  There are default values for `x` at `A`, `B`, and `C`.
+  We say the default value at `C` has distance 0, the one at `B` distance 1, and the one at `A`
+  distance 2.
+  The field `maxDistance` specifies the maximum distance considered in a round of Default field
+  computation.
+  Remark: since `C` does not set a default value of `y`, the default value at `B` is at distance 0.
+  The fixpoint for setting default values works in the following way.
+  - Keep computing default values using `maxDistance == 0`.
+  - We increase `maxDistance` whenever we failed to compute a new default value in a round.
+  - If `maxDistance > 0`, then we interrupt a round as soon as we compute some default value.
+    We use depth-first search.
+  - We sign an error if no progress is made when `maxDistance` == structure hierarchy depth (2 in
+    the example above).
+  -/
+  maxDistance : Nat := 0
+
+/-- Stores an indicator of whether progress has been made during a round in the default loop. -/
+structure State where
+  /-- Indicates whether progress has been made during a round in the default loop. -/
+  progress : Bool := false
+
+/-- Collects the names of all nested structures in a `Struct` (at any depth), including the name of
+    the structure itself. -/
+partial def collectStructNames (struct : Struct) (names : Array Name) : Array Name :=
+  let names := names.push struct.structName
+  struct.fields.foldl (init := names) fun names field =>
+    match field.val with
+    | .nested struct => collectStructNames struct names
+    | _ => names
+
+/-- Gets the maximum depth at which any structure is nested within the given structure, i.e. the
+    height of its subobject poset. -/
+partial def getHierarchyDepth (struct : Struct) : Nat :=
+  struct.fields.foldl (init := 0) fun max field =>
+    match field.val with
+    | .nested struct => Nat.max max (getHierarchyDepth struct + 1)
+    | _ => max
+
+/-- (Monadic) Checks if the value of a field (`expr?`) is an unassigned metavariable that is
+    annotated to indicate that it should be synthesized during the default loop. -/
+def isDefaultMissing? [Monad m] [MonadMCtx m] (field : Field Struct) : m Bool := do
+  if let some expr := field.expr? then
+    if let some (.mvar mvarId) := defaultMissing? expr then
+      unless (← mvarId.isAssigned) do
+        return true
+  return false
+
+/-- (Monadic) Gets the first encountered field in a `Struct` whose value (`expr?`) is an unassigned
+    metavariable that is annotated to indicate that it should be synthesized during the default
+    loop. -/
+partial def findDefaultMissing? [Monad m] [MonadMCtx m] (struct : Struct) :
+m (Option (Field Struct)) :=
+  struct.fields.findSomeM? fun field => do
+   match field.val with
+   | .nested struct => findDefaultMissing? struct
+   | _ => return if (← isDefaultMissing? field) then field else none
+
+/-- (Monadic) Gets an array containing all fields in the `Struct` whose value (`expr?`) is an
+    unassigned metavariable that is annotated to indicate that it should be synthesized during the
+    default loop. -/
+partial def allDefaultMissing [Monad m] [MonadMCtx m] (struct : Struct) :
+m (Array (Field Struct)) :=
+  go struct *> get |>.run' #[]
+where
+  /-- Loop through all fields in the `Struct`, recursing if a `.nested` one is found, and storing
+      the field in a mutable array if it `isDefaultMissing?` -/
+  go (struct : Struct) : StateT (Array (Field Struct)) m Unit :=
+    for field in struct.fields do
+      if let .nested struct := field.val then
+        go struct
+      else if (← isDefaultMissing? field) then
+        modify (·.push field)
+
+/-- Gets the name of a field, assuming that its `lhs` is of the form `[.fieldName _ fieldName]`.
+    Panics otherwise. -/
+def getFieldName (field : Field Struct) : Name :=
+  match field.lhs with
+  | [.fieldName _ fieldName] => fieldName
+  | _ => unreachable!
+
+/-- Abbreviation for `ReaderT Context (StateRefT State TermElabM)`: A monad transformation of
+    `TermElabM` that lets us access the `Context` (relevant for checking if default values are
+    overridden) and keeping track of whether progress has been made during a round of the default
+    loop (`State`). -/
+abbrev M := ReaderT Context (StateRefT State TermElabM)
+
+/-- Checks if the round has completed by checking that progress has been made and that the
+    `maxDistance > 0`. -/
+def isRoundDone : M Bool := do
+  return (← get).progress && (← read).maxDistance > 0
+
+/-- Gets the value (`expr?`) of a field in a `Struct` given the name of the field. -/
+def getFieldValue? (struct : Struct) (fieldName : Name) : Option Expr :=
+  struct.fields.findSome? fun field =>
+    if getFieldName field == fieldName then
+      field.expr?
+    else
+      none
+
+section NamedGoalsWithMetadata
+/-- A convenient representation of the metadata attached to named goals produced by `?..` syntax. -/
+structure FieldHoleMData where
+  /-- The index of the named goal used for name conflict resolution when dealing with multiple
+      occcurrences of `?..`. Each conflicting use of `?..` should generate field holes with
+      different indices. An index of `0` indicates that no name conflicts were found with any
+      existing goals. -/
+  index      : Nat
+  /-- The syntax of the structure instance that contained the `?..` syntax. -/
+  structRef  : Syntax
+  /-- The name of the structure that contained the `?..` syntax. -/
+  structName : Name
+  /-- The name of the field this goal represents. -/
+  fieldName  : Name
+  /-- The name to be prefixed to the name of this goal. `Name.anonymous` indicates that no name is
+      to be prefixed. -/
+  prefixName : Name
+
+/-- Creates the metadata for a field's named goal given the field, the `Struct`, and the
+    conflict-resolution index. -/
+def mkFieldHoleMData (index : Nat) (field : Field Struct) (struct : Struct) : FieldHoleMData :=
+  {
+    index,
+    structRef  := struct.ref
+    structName := struct.structName
+    fieldName  := getFieldName field
+    prefixName := match struct.source.implicit with
+                  | some {name := some prefixName, ..} => prefixName
+                  | _ => Name.anonymous
+  }
+
+open KVMap in
+/-- Gets the field hole metadata from a metavariable if present. -/
+def getFieldHoleMDataFromMVar? (decl : MetavarDecl) : Option FieldHoleMData :=
+  match decl.type with
+  | .mdata md _ =>
+    if getBool md `fieldHole then
+      some
+      {
+        index      := getNat md `index
+        structRef  := getSyntax md `structRef
+        structName := getName md `structName
+        fieldName  := getName md `fieldName
+        prefixName := getName md `prefixName
+      }
+    else none
+  | _ => none
+
+/-- Checks if a metavariable decl is a named field hole created by `?..` syntax. -/
+def isFieldHole (decl : MetavarDecl) : Bool :=
+  match decl.type with
+  | .mdata md _ => KVMap.getBool md `fieldHole
+  | _           => false
+
+section KVMap
+/-- Merges two `KVMap`s, overwriting the values of any shared keys with those in the second `KVMap`
+    -/
+def mergeKVMap : KVMap → KVMap → KVMap :=
+  fun m₀ m₁ => Id.run do
+    let mut m := m₀
+    for (name, data) in m₁ do
+      m := KVMap.insert m name data
+    return m
+
+/-- Turns a list of key-value pairs (e.g. ``[(`a, ofBool true), (`b, ofNat 2), ...]``) into a
+    `KVMap`. -/
+def toKVMap : List (Name × DataValue) → KVMap
+| l => l.foldl (fun m (n, d) => KVMap.insert m n d) {}
+
+end KVMap
+
+open DataValue in
+/-- Turns a representation of field hole metadata into actual metadata (a `KVMap`). -/
+def mkFieldHoleMDataKVMap (f : FieldHoleMData) : KVMap :=
+  toKVMap [
+    (`fieldHole  , ofBool   true        ),
+    (`index      , ofNat    f.index     ),
+    (`structRef  , ofSyntax f.structRef ),
+    (`structName , ofName   f.structName),
+    (`fieldName  , ofName   f.fieldName ),
+    (`prefixName , ofName   f.prefixName)
+  ]
+
+/--
+  Create a metavariable with `metadata` attached to its `type`.
+  If there's any existing metadata on `type`, `metadata` is preferentially merged into it.
+  -/
+def mkFreshExprMVarWithMData (type : Expr) (metadata : KVMap) (kind : MetavarKind := default)
+(userName := Name.anonymous) : MetaM Expr :=
+  let annotatedType :=
+    match type with
+    | .mdata m e =>
+      let merge := mergeKVMap m metadata
+      Expr.mdata merge e
+    | _          =>
+      Expr.mdata metadata type
+  mkFreshExprMVar annotatedType (kind := kind) (userName := userName)
+
+/-- Make a fresh expression metavariable for a field, named accordingly, and with metadata
+    attached. -/
+def mkFreshFieldNamedMVar (type : Expr) (index : Nat) (prefixName : Option Name)
+(field : Field Struct) (struct : Struct) : MetaM Expr :=
+  let fieldHoleMData := mkFieldHoleMDataKVMap <| mkFieldHoleMData index field struct
+  let name :=
+    match prefixName with
+    | some x => x ++ (getFieldName field)
+    | none   => getFieldName field
+  let name := if index == 0 then name else name.appendIndexAfter index
+  mkFreshExprMVarWithMData type fieldHoleMData (kind := .syntheticOpaque) (userName := name)
+
+/-- Given the names of two structures, check if they have any field names in common. -/
+def fieldsOverlap (env : Environment) (structName₀ : Name) (structName₁ : Name) : Bool :=
+  let fields₀ := getStructureFieldsFlattened env structName₀ false
+  let fields₁ := getStructureFieldsFlattened env structName₁ false
+  fields₀.any (fun field => fields₁.contains field)
+
+-- Monadic to enable tracing.
+/-- If the provided metavariable decl is a named field hole created by `?..` syntax, check if it
+    conflicts with the current structure and prefix name. If so, return its index. Otherwise,
+    return `none`. -/
+def getConflictingIndex? (env : Environment) (s : Struct) (prefixName : Name) (decl : MetavarDecl)
+: TermElabM (Option Nat) := do
+  let fieldHoleMData? := getFieldHoleMDataFromMVar? decl
+  match fieldHoleMData? with
+  | some fieldHoleMData =>
+    let cond2 := prefixName == fieldHoleMData.prefixName
+    let cond3 := fieldsOverlap env s.structName (fieldHoleMData.structName)
+    trace[Elab.struct]
+      "goal name conflict for {fieldHoleMData.structName}: {cond2} && {cond3}"
+    if cond2 && cond3
+    then return some fieldHoleMData.index
+    else return none
+  | none => return none
+
+/-- Get the next non-conflicting index among all metavariable conflicts.
+    A metavariable conflicts iff all of the following are true:
+    * it is a named field hole created by `?..` syntax
+    * it is not from the same occurrence of `?..`
+    * it has the same prefix name (possibly `Name.anonymous` if it does not have a prefix)
+    * it belongs to a structure that has field names in common with the current structure
+    Note that this gets the index one greater than the maximum conflicting index, not the next
+    "available" index. We take a "wide berth" approach to avoid situations where it might appear
+    like two goals are from the same occurrence of `?..` despite this not being the case. -/
+def nextIndexGivenCollisions (env : Environment) (mctx : MetavarContext) (s : Struct)
+: TermElabM Nat := do
+  let prefixName := match s.source.implicit with
+  | some { name := some prefixName, .. } => prefixName
+  | _ => Name.anonymous
+  let conflictingIndex : (Option Nat) ← mctx.decls.foldl
+    (fun i? _ decl => do
+      let i'? ← getConflictingIndex? env s prefixName decl
+      return (Option.merge max (← i?) i'?)) (pure none)
+  match conflictingIndex with
+  | some i => return i+1
+  | none   => return 0
+
+/-- Assign all fields which did not get synthesized during the default loop (but which were marked
+    as such) to appropriately-named field holes with metadata in the case of `?..` syntax (and to
+    natural holes when the `?` is absent). -/
+def assignRemainingDefaultsToFieldHoles (struct : Struct) : TermElabM Unit :=
+  withRef struct.ref do
+  match struct.source.implicit with
+  | some vhc =>
+    let index ← nextIndexGivenCollisions (← getEnv) (← getMCtx) struct
+    for field in (← allDefaultMissing struct) do
+      match field.expr? with
+      | some expr =>
+        match defaultMissing? expr with
+        | some (.mvar mvarId) =>
+          let type := (← getMVarDecl mvarId).type
+          if vhc.isSynthetic then
+            mvarId.assign (← withRef field.ref <|
+              mkFreshFieldNamedMVar type index vhc.name field struct)
+          else
+            let newHole ← withRef field.ref <| mkFreshExprMVar type (kind := .natural)
+            mvarId.assign newHole
+            registerMVarErrorHoleInfo newHole.mvarId! struct.ref
+        | _ => unreachable!
+      | none => unreachable!
+  | none => return ()
+
+end NamedGoalsWithMetadata
+/-- A helper function that applies lambdas whose parameters are field names to the corresponding
+    field values until it finds a non-lambda, using propagated parameters instead of field names if
+    necessary along the way. Returns `none` if it finds a lambda that's not of this form. -/
+partial def mkDefaultValueAux? (struct : Struct) : Expr → TermElabM (Option Expr)
+  | .lam n d b c => withRef struct.ref do
+    if c.isExplicit then
+      let fieldName := n
+      match getFieldValue? struct fieldName with
+      | none     => return none
+      | some val =>
+        let valType ← inferType val
+        if (← isDefEq valType d) then
+          mkDefaultValueAux? struct (b.instantiate1 val)
+        else
+          return none
+    else
+      if let some (_, param) := struct.params.find? fun (paramName, _) => paramName == n then
+        -- Recall that we did not use to have support for parameter propagation here.
+        if (← isDefEq (← inferType param) d) then
+          mkDefaultValueAux? struct (b.instantiate1 param)
+        else
+          return none
+      else
+        let arg ← mkFreshExprMVar d
+        mkDefaultValueAux? struct (b.instantiate1 arg)
+  | e =>
+    if e.isAppOfArity ``id 2 then
+      return some e.appArg!
+    else
+      return some e
+
+/-- If possible, make a default value by applying lambdas in the given constant to the appropriate
+    field values or propagated parameter values. -/
+def mkDefaultValue? (struct : Struct) (cinfo : ConstantInfo) : TermElabM (Option Expr) :=
+  withRef struct.ref do
+  let us ← mkFreshLevelMVarsFor cinfo
+  mkDefaultValueAux? struct (← instantiateValueLevelParams cinfo us)
+
+/-- Reduce default value. It performs beta reduction and projections of the given structures. -/
+partial def reduce (structNames : Array Name) (e : Expr) : MetaM Expr := do
+  match e with
+  | .lam ..       => lambdaLetTelescope e fun xs b => do mkLambdaFVars xs (← reduce structNames b)
+  | .forallE ..   => forallTelescope e fun xs b => do mkForallFVars xs (← reduce structNames b)
+  | .letE ..      => lambdaLetTelescope e fun xs b => do mkLetFVars xs (← reduce structNames b)
+  | .proj _ i b   =>
+    match (← Meta.project? b i) with
+    | some r => reduce structNames r
+    | none   => return e.updateProj! (← reduce structNames b)
+  | .app f .. =>
+    match (← reduceProjOf? e structNames.contains) with
+    | some r => reduce structNames r
+    | none   =>
+      let f := f.getAppFn
+      let f' ← reduce structNames f
+      if f'.isLambda then
+        let revArgs := e.getAppRevArgs
+        reduce structNames (f'.betaRev revArgs)
+      else
+        let args ← e.getAppArgs.mapM (reduce structNames)
+        return mkAppN f' args
+  | .mdata _ b =>
+    let b ← reduce structNames b
+    if (defaultMissing? e).isSome && !b.isMVar then
+      return b
+    else
+      return e.updateMData! b
+  | .mvar mvarId =>
+    match (← getExprMVarAssignment? mvarId) with
+    | some val => if val.isMVar then pure val else reduce structNames val
+    | none     => return e
+  | e => return e
+
+/--
+  Attempt to synthesize the default value for a field, looping through nested structures if
+  necessary. If a default value is found, assign it to the metavariable that we created for the
+  field's value back in `elabStruct`, and return `true`. Otherwise return `false`.
+-/
+partial def tryToSynthesizeDefault (structs : Array Struct) (allStructNames : Array Name)
+(maxDistance : Nat) (fieldName : Name) (mvarId : MVarId) : TermElabM Bool :=
+  let rec loop (i : Nat) (dist : Nat) := do
+    if dist > maxDistance then
+      return false
+    else if h : i < structs.size then
+      let struct := structs.get ⟨i, h⟩
+      match getDefaultFnForField? (← getEnv) struct.structName fieldName with
+      | some defFn =>
+        let cinfo ← getConstInfo defFn
+        let mctx ← getMCtx
+        match (← mkDefaultValue? struct cinfo) with
+        | none     => setMCtx mctx; loop (i+1) (dist+1)
+        | some val =>
+          let val ← reduce allStructNames val
+          match val.find? fun e => (defaultMissing? e).isSome with
+          | some _ => setMCtx mctx; loop (i+1) (dist+1)
+          | none   =>
+            let mvarDecl ← getMVarDecl mvarId
+            let val ← ensureHasType mvarDecl.type val
+            mvarId.assign val
+            return true
+      | _ => loop (i+1) dist
+    else
+      return false
+  loop 0 0
+
+/-- The main loop of `tryToSynthesizeDefault`, which keeps track of which struct out of an array of
+    all nested structs is being considered, as well as the distance to make sure it doesn't exceed
+    the `maxDistance` (see the documentation for `Context.maxDistance`). -/
+add_decl_doc tryToSynthesizeDefault.loop
+
+/--
+  A step within the default synthesis loop. We proceed only if the round is not done. We loop
+  through all fields in the structure, attempting to synthesize a default via
+  `tryToSynthesizeDefault` when possible. If we succeed, we set `progress := true` in the `State`.
+  Note: by now, all `expr?`s should be `some expr` from `elabStruct`, even if that `expr` is a
+  metavariable; as such, we panic if one of them is `none`.
+-/
+partial def step (struct : Struct) : M Unit :=
+  unless (← isRoundDone) do
+    withReader (fun ctx => { ctx with structs := ctx.structs.push struct }) do
+      for field in struct.fields do
+        match field.val with
+        | .nested struct => step struct
+        | _ => match field.expr? with
+          | none      => unreachable!
+          | some expr =>
+            match defaultMissing? expr with
+            | some (.mvar mvarId) =>
+              unless (← mvarId.isAssigned) do
+                let ctx ← read
+                if (← withRef field.ref (tryToSynthesizeDefault
+                  ctx.structs ctx.allStructNames ctx.maxDistance (getFieldName field) mvarId))
+                then
+                  modify fun _ => { progress := true }
+            | _ => pure ()
+
+/--
+  The workhorse of the default synthesis loop.
+  If there are no fields left that need to be synthesized during the default loop, we return from
+  the loop.
+  Otherwise, when we find a field that ought to be synthesized during the default loop, we take a
+  `step`. If we've made `progress`, we call `propagateLoop` again and reset the depth to `0`. If we
+  haven't, we call `propagateLoop` again with a higher depth.
+  If the depth ever exceeds the hierarchy depth, we know that we've searched all nested structures,
+  but no default values were to be found. In this case, we either throw an error with the missing
+  fields, or, if a variadic hole is present (e.g. `?..`), simply return from the loop (at which
+  point the remaining holes will be assigned by `assignRemainingDefaultsToFieldHoles` ).
+-/
+partial def propagateLoop (hierarchyDepth : Nat) (d : Nat) (struct : Struct) : M Unit := do
+  match (← findDefaultMissing? struct) with
+  | none       => return () -- Done
+  | some field =>
+    trace[Elab.struct] "propagate [{d}] [field := {field}]: {struct}"
+    if d > hierarchyDepth then
+      let missingFields := (← allDefaultMissing struct).map getFieldName
+      if struct.source.implicit.isSome then
+        return ()
+      else
+        let missingFieldsWithoutDefault :=
+        let env := (← getEnv)
+        let structs := (← read).allStructNames
+        missingFields.filter fun fieldName => structs.all fun struct =>
+          (getDefaultFnForField? env struct fieldName).isNone
+        let fieldsToReport :=
+          if missingFieldsWithoutDefault.isEmpty then missingFields else missingFieldsWithoutDefault
+        throwErrorAt field.ref
+          "fields missing: {fieldsToReport.toList.map (s!"'{·}'") |> ", ".intercalate}"
+    else withReader (fun ctx => { ctx with maxDistance := d }) do
+      modify fun _ => { progress := false }
+      step struct
+      if (← get).progress then
+        propagateLoop hierarchyDepth 0 struct
+      else
+        propagateLoop hierarchyDepth (d+1) struct
+
+/--
+  The default synthesis loop.
+  We call our workhorse function `propagateLoop` with appropriate initial values, which implements
+  the loop itself (unless there is a variadic hole that specifies defaults are not to be used).
+  Then, if there is a variadic hole, we assign the remaining metavariables that couldn't be
+  synthesized into default values to (named) field holes.
+-/
+def propagate (struct : Struct) : TermElabM Unit := do
+  let hierarchyDepth := getHierarchyDepth struct
+  let structNames := collectStructNames struct #[]
+  let vhc? := struct.source.implicit
+  if vhc?.all (·.useDefaults) then
+    propagateLoop hierarchyDepth 0 struct { allStructNames := structNames } |>.run' {}
+  if vhc?.isSome then
+    assignRemainingDefaultsToFieldHoles struct
+
+end ImplicitFields
+
+/--
+  The main content of the elaboration, during which we normalize the `Struct`'s form, call
+  `elabStruct` to compute field values and construct the elaborated expression, run the default
+  synthesis loop (and provide named field holes if warranted), and synthesize instances. -/
+private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (source : Source)
+: TermElabM Expr := do
+  let structName ← getStructName expectedType? source
+  let struct ← liftMacroM <| mkStructView stx structName source
+  let struct ← expandStruct struct
+  trace[Elab.struct] "{struct}"
+  /- We try to synthesize pending problems with `withSynthesize` combinator before trying to use
+     default values.
+     This is important in examples such as
+      ```
+      structure MyStruct where
+          {α : Type u}
+          {β : Type v}
+          a : α
+          b : β
+      #check { a := 10, b := true : MyStruct }
+      ```
+     were the `α` will remain "unknown" until the default instance for `OfNat` is used to ensure
+     that `10` is a `Nat`.
+     TODO: investigate whether this design decision may have unintended side effects or produce
+     confusing behavior.
+  -/
+  let { val := r, struct, instMVars } ← withSynthesize (mayPostpone := true) <|
+    elabStruct struct expectedType?
+  trace[Elab.struct] "before propagate {r}"
+  ImplicitFields.propagate struct
+  synthesizeAppInstMVars instMVars r
+  return r
+
+/-- The term elaborator for structure instance syntax that includes variadic holes (`?..`). -/
+@[term_elab structInstWithHoles] def elabStructInstWithHoles : TermElab := fun stx expectedType? =>
+do
+  match (← expandNonAtomicExplicitSources stx) with
+  | some stxNew => withMacroExpansion stx stxNew <| elabTerm stxNew expectedType?
+  | none =>
+    let sourceView ← getStructSource stx
+    if let some modifyOp ← isModifyOp? stx then
+      if sourceView.explicit.isEmpty then
+        throwError
+          "invalid \{...} notation, explicit source is required when using '[<index>] := <value>'"
+      elabModifyOp stx modifyOp sourceView.explicit expectedType?
+    else
+      elabStructInstAux stx expectedType? sourceView
+
+section haveFieldProj
+
+/-- `as foo` names the field projection `foo`. -/
+declare_syntax_cat asname
+/-- `as foo` names the field projection `foo`. -/
+syntax "as" ident : asname
+
+-- couldn't write elab "haveFieldProj" f:(ident)? x:("as" n:ident)? : tactic
+/--
+  Once a goal has been created for a structure's field via `?..` syntax, `haveFieldProj` can be
+  used equivalently to `have <field name>.proj := <projection function>`.
+  `haveFieldProj f as a` gets the field projection for the field `f` and names it `a`;
+  `f` and `as a` can both be individually omitted.
+-/
+elab "haveFieldProj" f:(ident)? x:(asname)? : tactic => do
+  let fieldHoleMData? := ImplicitFields.getFieldHoleMDataFromMVar? (← Tactic.getMainDecl)
+  match fieldHoleMData? with
+  | some fieldHoleMData =>
+    let fieldName := match f with | some f' => f'.getId | none => fieldHoleMData.fieldName
+    let structName := fieldHoleMData.structName -- so the error fits on one line
+    let some projname :=
+      (getProjFnForField? (← getEnv) fieldHoleMData.structName fieldName) | throwError
+        "couldn't find projection function for field {fieldName} of structure {structName}"
+    let name := match x with
+      | some stx => match stx with
+        | `(asname|as $n:ident) => n
+        | _ => mkIdent (fieldName ++ `proj)
+      | none => mkIdent (fieldName ++ `proj)
+    Tactic.evalTactic (←`(tactic|have $name := $(mkIdent projname)))
+  | none => throwError "no field metadata found on the main goal"
+
+end haveFieldProj
diff --git a/server/adam/Adam/StructInstWithHolesTest.lean b/server/adam/Adam/StructInstWithHolesTest.lean
new file mode 100644
index 0000000..12fdc8d
--- /dev/null
+++ b/server/adam/Adam/StructInstWithHolesTest.lean
@@ -0,0 +1,117 @@
+import Adam.StructInstWithHoles
+import Mathlib
+
+
+example : Module ℚ ℝ := by
+  refine { ?..! }
+  exact fun a r => a * r
+  intro b
+  sorry
+  sorry
+  sorry
+  sorry
+  sorry
+  sorry
+  sorry
+
+structure Foo where
+  x : Nat := 0
+  y : Nat
+
+structure Bar extends Foo where
+  z : Nat := x
+
+example := by refine { ?.. : Foo }; case y => exact 0
+example := by refine { ?.. : Bar }; case y => exact 0
+example := by refine { ?..a : Bar }; case a.y => exact 0
+example := by refine { ?..! : Bar }; case x | y | z => exact 0;
+example := by refine { ?..!a : Bar }; case a.x | a.y | a.z => exact 0;
+-- example := by refine' { ... : Bar }; exact 0
+example := by refine' { .. : Bar };  exact 0; exact 0; exact 0
+-- example := by refine' { ..! : Bar }; exact 0; exact 0; exact 0
+
+structure rflFoo where
+  x  : Nat
+  y  : Nat
+  xy : x = y := by rfl
+
+example := by refine { ?.. : rflFoo }; (case x | y => exact 0); case xy => rfl
+example := by refine { ?..! : rflFoo }; (case x | y => exact 0); case xy => rfl
+
+structure autoFoo where
+  x  : Nat := 0
+  y  : Nat := 0
+  xy : x = y := by rfl
+
+example := { ?.. : autoFoo }
+example := by refine { ?..! : autoFoo }; (case x | y => exact 0); case xy => rfl
+
+def f : Foo → Nat := fun _ => 0
+def ff : Foo → Foo → Unit := fun _ _ => ()
+def ffb : Foo → Bar → Unit := fun _ _ => ()
+def ffa : Foo → autoFoo → Unit := fun _ _ => ()
+
+example := by refine { x := f { ?.. }, ?.. : Foo }; case y | y_1 => exact 0
+example := by refine { x := f { ?..x }, ?.. : Foo }; case x.y | y => exact 0
+example := by refine { x := f { ?.. }, ?..x : Foo }; case y | x.y => exact 0
+example := by refine { x := f { ?..x }, ?..x : Foo }; case x.y | x.y_1 => exact 0
+
+example := by refine ff { ?.. } { ?.. }; case y | y_1 => exact 0
+example := by refine ff { ?..! } { ?.. }; case x | y | y_1 => exact 0
+example := by refine ffb { ?..! } { ?..! }; case x | y | x_1 | y_1 | z_1 => exact 0
+example := by refine ffa { ?..! } { ?..! }; (case x | y | x_1 | y_1 => exact 0); rfl
+
+structure Foo' where
+  x : Nat
+
+structure dFoo' where
+  x : Nat := 0
+
+def ff' : Foo → Foo' → Unit := fun _ _ => ()
+def fdf' : Foo → dFoo' → Unit := fun _ _ => ()
+
+example := by refine ff' { ?.. } { ?.. }; case y | x_1 => exact 0
+example := by refine fdf' { ?.. } { ?.. }; case y => exact 0
+
+structure Fooα (α : Type) where
+  x : α
+
+example := by refine { ?.. : Fooα Nat}; case x => exact 0
+
+structure Fooαi where
+  {α : Type}
+  x : α
+
+example := by refine { ?.. : Fooαi }; (case α => exact Nat); case x => exact 0
+
+/- haveFieldProj tests (subject to be moved)-/
+section haveFieldProj
+
+structure Foo'' where
+  x : Bool
+  y : Nat
+
+def foo'': Foo'' := { x := true, y := 0 }
+
+example := by
+  refine { ?.. : Foo''};
+  haveFieldProj;
+  case x => exact x.proj foo'';
+  case y => exact 0
+example := by
+  refine { ?.. : Foo''};
+  haveFieldProj as a;
+  case x => exact a foo'';
+  case y => exact 0
+example := by
+  refine { ?.. : Foo''};
+  haveFieldProj y;
+  case x => exact 0 == y.proj foo'';
+  case y => exact 0
+example := by
+  refine { ?.. : Foo''};
+  haveFieldProj y as a;
+  case x => exact 0 == a foo'';
+  case y => exact 0
+
+end haveFieldProj
diff --git a/server/adam/Adam/TacticDocs.lean b/server/adam/Adam/TacticDocs.lean
new file mode 100644
index 0000000..6a3b96d
--- /dev/null
+++ b/server/adam/Adam/TacticDocs.lean
@@ -0,0 +1,566 @@
+import GameServer.Commands
+import Adam.Tactics
+
+TacticDoc assumption
+"
+`assumption` sucht nach einer Annahme, die genau dem Goal entspricht.
+
+## Beispiel
+
+`assumption` sucht durch die Annahmen und merkt dass `h` genau mit dem Goal übereinstimmt.
+
+```
+Objekte
+  a b c d : ℕ
+  h : a + b = c
+  g : a * b = 16
+  t : c = 12
+Goal
+  a + b = c
+```
+"
+
+TacticDoc apply
+"
+`apply my_lemma` Versucht das Goal mit der Aussage des Lemmas zu unifizieren
+und erstellt ein neues Goal pro Annahme des Lemmas, die noch zu zeigen ist.
+
+## Details
+`apply` funktioniert gleichermassen für Lemmas wie für Implikationen
+wie z.B. `(h : A → B)`.
+
+## Beispiel
+
+Gegeben folgendes Lemma:
+```
+lemma Nat.eq_zero_of_le_zero {n : ℕ} (h : n ≤ 0) : n = 0 := by sorry
+```
+
+Und folgendes Problem:
+
+```
+
+Objekte
+  n : ℕ
+  ...
+Goal
+  n = 0
+```
+
+Hier ändert `apply Nat.eq_zero_of_le_zero` das Goal zu `n ≤ 0` durch Anwendung
+des Lemmas.
+"
+
+TacticDoc by_cases
+"
+`by_cases h : P` macht eine Fallunterscheidung. Im ersten Goal wird eine Annahme
+`(h : P)` hinzugefügt, im zweiten `(h : ¬P)`.
+
+## Details
+
+`P` kann eine beliegige Aussage sein, die als entweder wahr oder falsch angenommen wird.
+
+## Beispiel
+
+```
+example (A : Prop) : A ∨ ¬ A := by
+  by_cases h : A
+  · left
+    assumption
+  · right
+    assumption
+```
+"
+
+TacticDoc by_contra
+"
+`by_contra h` startet einen Widerspruchsbeweis.
+
+## Details
+Sei `P` das aktuelle Goal. `by_contra h` fügt eine neue Annahme `(h : ¬P)` hinzu
+und setzt das Goal auf `False`.
+
+Oft will man `by_contra` nutzen wenn das Goal von der Form `¬ P` ist.
+
+## Hilfreiche Resultate
+
+* `contradiction` schliesst den Widerspruchsbeweis wenn sich (zwei) Annahmen
+widersprechen.
+* `contrapose` führt einen Beweis durch Kontraposition und ist entsprechend
+in ähnlichen Situationen nutzbar wie `by_contra`
+"
+
+TacticDoc change
+"
+`change t` ändert das Goal zu `t`. Voraussetzung ist, dass `t` und das alte Goal defEq sind.
+
+## Details
+
+Dies ist insbesonder hilfreich wenn eine Taktik nicht merkt, dass das Goal defEq ist zu einem
+Term, der eigentlich gebraucht würde.
+
+## Beispiel
+
+Aktuelles Goal:
+
+```
+b: ℝ
+⊢ 1 • b = b
+```
+Wobei die Skalarmultiplikation als `fun (a : ℚ) (r : ℝ) => ↑a * r` definiert war. Dann
+kann man mit `change (1 : ℚ) * b = b` das Goal umschreiben und anschliessend mit Lemmas
+über die Multiplikation beweisen.
+"
+
+TacticDoc constructor
+"
+`constructor` teilt ein Goal auf, wenn das Goal eine Struktur ist
+
+## Detail
+Wenn das Goal eine Struktur ist, wie z.B. `A ∧ B` welches zwei Felder hat `⟨A, B⟩`, dann
+erzeugt `constructor` ein Goal pro Feld der Struktur.
+
+## Hilfreiche Resultate
+
+* Das Gegenteil von `constructor` ist `⟨_, _⟩` (`\\<>`), der *anonyme Konstructor*.
+Dieser enspricht ungefähr der Tupel-Notation in
+\"eine Gruppe ist ein Tupel $(G, 0, +)$, sodass …\".
+
+## Beispiel
+
+```
+example {A B : Prop} (h : A) (g : B) : A ∧ B := by
+  constructor
+  · assumption
+  · assumption
+```
+"
+
+TacticDoc contradiction
+"
+`contradiction` schliesst den Beweis wenn es einen Widerspruch in den Annahmen findet.
+
+## Details
+Ein Widerspruch in den Annahmen kann unter anderem folgendermassen aussehen:
+
+* `(h : n ≠ n)`
+* `(h : A)` und `(h' : ¬A)`
+* `(h : False)` (i.e. ein Beweis von `False`)
+
+## Beispiel
+
+Folgenes Goal wird von `contradiction` bewiesen
+
+## Hilfreiche Resultate
+
+* Normalerweise wird `contradiction` gebraucht um einen Widerspruchsbeweis zu
+  schliessen, der mit `by_contra` eröffnet wurde.
+* Ein Beweis von `False` representiert in Lean einen Widerspruch.
+
+```
+Objekte:
+  (n m : ℕ)
+  (h : n = m)
+  (g : n ≠ m)
+Goal
+  37 = 60
+```
+nach dem Motto \"ein Widerspruch beweist alles.\"
+"
+
+TacticDoc contrapose
+"
+`contrapose` ändert ein Goal der Form `A → B` zu `¬B → ¬A` und führt damit
+eine Beweis durch Kontraposition.
+
+## Hilfreiche Resultate
+
+* `revert h` kann nützlich sein um eine Annahme als Implikationsprämisse zu schreiben bevor man
+  `contrapose` verwendet.
+"
+
+TacticDoc exact
+"
+`exact h` schliesst das Goal wenn der Term `h` mit dem Goal übereinstimmt.
+"
+
+TacticDoc fin_cases
+"
+`fin_cases i` führt eine Fallunterscheidung wenn `i` ein endlicher Typ ist.
+
+## Details
+`fin_cases i` ist insbesondere nützlich für `(i : Fin n)`, zum Beispiel als Index in
+endlich dimensionalen Vektorräumen.
+
+In diesem Fall bewirkt `fin_cases i` dass man Komponentenweise arbeitet.
+"
+
+TacticDoc funext
+"
+`funext x` wird bei Gleichungen von Funktionen `f = g` gebraucht. Das Goal wird zu
+`f x = g x`.
+
+## Details
+Nach dem Motto `f = g ↔ ∀ x, f x = g x` sind zwei Funktionen dann identisch, wenn sie
+angewendet auf jedes Element identisch sind. `funext x` benützt dieses Argument.
+"
+
+TacticDoc «have»
+"
+`have h : P` führt ein Zwischenresultat ein.
+
+## Details
+Anschliessend muss man zuerst dieses Zwischenresultat beweisen bevor man mit dem Beweis
+weitermachen und das Zwischenresultat verwenden kann.
+
+## Hilfreiche Resultate
+
+* `suffices h : P` funktioniert genau gleich, aussert das die beiden entstehenden Beweise
+  vertauscht sind.
+* `let h : Prop := A ∧ B` ist verwandt mit `have`, mit Unterschied, dass man mit `let`
+  eine temporäre Definition einführt.
+"
+
+TacticDoc induction
+"
+`induction n` führt einen Induktionsbeweis über `n`.
+
+## Detail
+
+Diese Taktik erstellt zwei Goals:
+* Induktionsanfang, wo `n = 0` ersetzt wird.
+* Induktionsschritt, in dem man die Induktionshypothese `n_ih` zur Verfügung hat.
+
+Der volle Syntax mit Option zum umbenennen der Induktionshypothes und -variable ist
+
+```
+induction n with
+| zero =>
+  sorry
+| succ m m_ih =>
+  sorry
+```
+
+da dieser sich über mehrere Zeilen erstreckt wird er im Spiel nicht eingeführt.
+
+## Hifreiche Resultate
+
+* `Nat.succ_eq_add_one`: schreibt `n.succ = n + 1` um.
+* `Nat.zero_eq`: schreibt `Nat.zero = 0` um.
+
+Beide sind DefEq, aber manche Taktiken können nicht damit umgehen
+
+* Siehe Definition `∑` für Hilfe mit Induktion über Summen.
+* `rcases n` ist sehr ähnlich zu `induction n`. Der Unterschied ist, dass bei
+`rcases` keine Induktionshypothese im Fall `n + 1` zur Verfügung steht.
+
+## Beispiel
+
+```
+example (n : ℕ) : 4 ∣ 5^n + 7 := by
+  induction n
+  sorry      -- Fall `n = 0`
+  sorry      -- Fall `n + 1`
+```
+"
+
+TacticDoc intro
+"
+`intro x` wird für Goals der Form `A → B` oder `∀ x, P x` verwendet.
+Dadurch wird die Implikationsprämisse (oder das Objekt `x`) den Annahmen hinzugefügt.
+
+## Hilfreiche Resultate
+
+* `revert h` macht das Gegenteil von `intro`.
+"
+
+TacticDoc left
+"
+Wenn das Goal von der Form `A ∨ B` ist, enscheidet man mit `left` die linke Seite zu zeigen.
+
+## Hilfreiche Resultate
+
+* `right` entscheidet sich für die linke Seite.
+"
+
+TacticDoc «let»
+"
+`let x : ℕ := 5 ^ 2` führt eine neue temporäre Definition ein.
+
+## Hilfreiche Resultate
+
+* `have x : ℕ := 5 ^ 2` führt ebenfalls eine neue natürliche Zahle `x` ein, aber
+  Lean vergisst sofort, wie die Zahl definiert war. D.h. `x = 25` wäre dann nicht
+  beweisbar. Mit `let x : ℕ := 5 ^ 2` ist `x = 25` durch `rfl` beweisbar.
+"
+
+TacticDoc linarith
+"
+`linarith` löst Systeme linearer (Un-)Gleichungen.
+
+## Detail
+`linarith` kann lineare Gleichungen und Ungleichungen beweisen indem
+es das Gegenteil vom Goal annimmt und versucht einen Widerspruch in den
+Annahmen zu erzeugen (Widerspruchsbeweis). Es braucht ein `≤` definiert um
+zu funktionieren.
+
+## Beispiel
+
+Folgendes kann `linarith` beweisen.
+```
+Objekte
+  x y : ℤ
+  h₁ : 5 * y ≤ 35 - 2 * x
+  h₂ : 2 * y ≤ x + 3
+Goal
+  y ≤ 5
+```
+"
+
+TacticDoc push_neg
+"
+`push_neg` schreibt `¬∀ x, _` zu `∃ x, ¬ _` und `¬∃ x, _` zu `∀x, ¬ _` um.
+
+## Details
+
+`psuh_neg` schiebt das `¬` soweit nach innen wie möglich.
+
+## Hilfreiche Resultate
+
+* Die beiden Lemmas heissen `not_forall` und `not_exists` und können mit `rw` einzeln angewendet
+  werden.
+"
+
+TacticDoc rcases
+"
+`rcases h` teilt eine Annahme `h` in ihre Einzelteile auf.
+
+## Details
+Für Annahmen die Strukturen sind, wie z.B. `h : A ∧ B` (oder `∃x, P x`) kann man die
+Einzelteile mit  `rcases h with ⟨a, b⟩` (oder `rcases h with ⟨x, hx⟩`) benennen.
+
+Für eine Annahme der Form `h : A ∨ B` kann man mit `rcases h with ha | hb` zwei Goals
+erzeugen, einmal unter Annahme der linken Seite, einmal unter Annahme der Rechten.
+
+## Hilfreiche Resultate
+
+* Für `n : ℕ` hat `rcases n` einen ähnlichen Effekt wie `induction n` mit dem Unterschied,
+  dass im Fall `n + 1` keine Induktionshypothese zur Verfügung steht.
+* In Lean gibt es auch die Taktik `cases`, die gleich funktioniert wie `rcases` aber
+  einen mehrzeiligen Syntax hat:
+  ```
+  cases h with
+  | inl ha =>
+    sorry
+  | inr hb =>
+    sorry
+  ```
+  Hier sind `inl`/`inr` die Namen der Fälle und `ha`/`hb` sind frei gewählte Namen für die
+  freien Variablen
+"
+
+TacticDoc refine
+"
+`refine { ?..! }` wird benötigt um eine Struktur (z.B. ein $R$-Modul) im Taktikmodus in einzelne
+Goals aufzuteilen. Danach hat man ein Goal pro Strukturfeld.
+
+(*Bemerkung*: Es gibt in Lean verschiedenste bessere Varianten dies zu erreichen,
+z.B. \"Term Modus\" oder \"anonyme Konstruktoren\", aber für den Zweck des Spieles bleiben wir
+bei diesem Syntax.)
+"
+
+TacticDoc revert
+"
+`revert h` fügt die Annahme `h` als Implikationsprämisse vorne ans Goal an.
+
+## Hilfreiche Resultate
+
+* `revert` ist das Gegenteil von `intro`.
+* `revert` kann insbesondere nützlich sein, um anschliessend `contrapose` zu verwenden.
+
+## Beispiel
+
+```
+Objekte
+  A P : Prop
+  h : P
+Goal
+  A
+```
+
+hier ändert `revert h` den Status zu
+
+```
+Objekte
+  A P : Prop
+Goal
+  P → A
+```
+"
+
+TacticDoc rfl
+"
+`rfl` beweist ein Goal der Form `X = X`.
+
+## Detail
+
+`rfl` beweist jedes Goal `A = B` wenn `A` und `B` per Definition das gleiche sind (DefEq).
+Andere Taktiken rufen `rfl` oft am Ende versteckt
+automatisch auf um zu versuchen, den Beweis zu schliessen.
+
+
+## Beispiel
+`rfl` kann folgende Goals beweisen:
+
+```
+Objekte
+  a b c : ℕ
+Goal:
+  (a + b) * c = (a + b) * c
+```
+
+```
+Objekte
+  n : ℕ
+Goal
+  1 + 1 = 2
+```
+denn Lean liest dies intern als `0.succ.succ = 0.succ.succ`.
+"
+
+TacticDoc right
+"
+Wenn das Goal von der Form `A ∨ B` ist, enscheidet man mit `right` die rechte Seite zu zeigen.
+
+## Hilfreiche Resultate
+
+* `left` entscheidet sich für die linke Seite.
+"
+
+TacticDoc ring
+"
+Löst Gleichungen mit den Operationen `+, -, *, ^`.
+
+## Details
+Insbesondere funktioniert `ring` in Ringen/Semiringen wie z.B. `ℕ, ℤ, ℚ, …`
+(i.e. Typen `R` mit Instanzen `Ring R` oder `Semiring R`).
+Die Taktik ist besonders auf kommutative Ringe (`CommRing R`) ausgelegt.
+
+## Hilfreiche Resultate
+
+* `ring` kann nicht wirklich mit Division (`/`) oder Inversen (`⁻¹`) umgehen. Dafür ist die
+  Taktik `field_simp` gedacht, und die typische Sequenz ist
+  ```
+  field_simp
+  ring
+  ```
+* Wenn `ring` nicht abschliesst, sagt es man solle `ring_nf` verwenden. Normalerweise heisst
+  das aber, dass man was falsch gemacht hat und die Seiten der Gleichung noch nicht gleich sind.
+"
+
+TacticDoc rw
+"
+Wenn man eine Annahme `(h : X = Y)` hat, kann man mit
+`rw [h]` alle `X` im Goal durch `Y` ersetzen.
+
+## Details
+
+* `rw [←h]` wendet `h` rückwärts an und ersetzt alle `Y` durch `X`.
+* `rw [h, g, ←f]`: Man kann auch mehrere `rw` zusammenfassen.
+* `rw [h] at h₂` ersetzt alle `X` in `h₂` zu `Y` (anstatt im Goal).
+
+`rw` funktioniert gleichermassen mit Annahmen `(h : X = Y)` also auch
+mit Theoremen/Lemmas der Form `X = Y`
+"
+
+TacticDoc simp
+"
+`simp` versucht alle Vereinfachungslemmas anzuwenden, die in der `mathlib` mit `@[simp]`
+gekennzeichnet sind.
+
+## Details
+
+* `simp?` zeigt welche Lemmas verwendet wurden.
+* `simp [my_lemma]` fügt zudem `my_lemma` temporär zur Menge der `simp`-Lemmas hinzu.
+* ein `simp`, das nicht am Ende des Beweis steht sollte durch eine entsprechende
+  `simp only [...]` Aussage ersetzt werden, um den Beweis stabiler zu machen.
+"
+
+TacticDoc simp_rw
+"
+`simp_rw [h₁, h₂, h₃]` versucht wie `rw` jedes Lemma der Reihe nach zu Umschreiben zu verwenden,
+verwendet aber jedes Lemma so oft es kann.
+
+## Details
+
+Es bestehen aber drei grosse Unterschiede zu `rw`:
+
+* `simp_rw` wendet jedes Lemma so oft an wie es nur kann.
+* `simp_rw` kann besser unter Quantifiern umschreiben als `rw`.
+* `simp_rw` führt nach jedem Schritt ein `simp only []` aus und vereinfacht dadurch grundlegenste
+  Sachen.
+"
+
+TacticDoc «suffices»
+"
+`suffices h : P` führt ein neues Zwischenresultat ein, aus dem das Goal direkt folgen soll.
+
+## Details
+
+Der einzige Unterschied zu `have h : P` ist, dass die beiden resultierenden Goals vertauscht sind.
+
+Mathematisch braucht man diese in ein bisschen unterschiedlichen Fällen:
+
+* `suffices h : P` : \"Es genügt zu zeigen, dass …\". Als erstes folgt die Erklärung wieso
+  das genügt, danach muss man nur noch `P` beweisen.
+* `have h : P` : Ein (kleines) Zwischenresultat. Als erstes folgt dann der Beweis dieses
+Resultats, anschliessend setzt man den Beweis mit Hilfe des Zwischenresultats fort.
+"
+
+TacticDoc tauto
+"
+## Beschreibung
+
+TODO
+"
+
+TacticDoc trivial
+"
+`trivial` versucht durch Kombination von wenigen simplen Taktiken das Goal zu schliessen.
+
+## Details
+Die Taktiken, die verwendet werden sind:
+
+* `assumption`
+* `rfl`
+* `contradiction`
+* und noch 3 andere, die hier nicht behandelt werden
+  (`decide`, `apply True.intro`, `apply And.intro`).
+"
+
+TacticDoc unfold
+"
+`unfold myDef` öffnet eine Definition im Goal.
+
+## Details
+Bis auf DefEq (definitinal equality) ändert `unfold` nichts, manche Taktiken
+(z.B. `push_neg`, `rw`) brauchen aber manchmal die Hilfe.
+
+`unfold myDef at h` kann auch Definitionen in Annahmen öffnen
+
+## Hilfreiche Resultate
+
+* `change P` ist eine andere Taktik, die das aktuelle Goal in einen DefEq-Ausdruck umschreibt.
+  Diese Taktik braucht man auch manchmal um zu hacken, wenn Lean Mühe hat etwas zu verstehen.
+"
+
+TacticDoc use
+"
+Wenn das Goal von der Form `∃x, P x` ist, kann man mit `use n` ein konkretes Element angeben
+mit dem man das Goal beweisen möchte.
+
+## Details
+
+`use n` versucht zudem anschliessend `rfl` aufzurufen, und kann das Goal damit manchmal direkt
+schließen.
+"
diff --git a/server/testgame/TestGame/Tactics.lean b/server/adam/Adam/Tactics.lean
similarity index 92%
rename from server/testgame/TestGame/Tactics.lean
rename to server/adam/Adam/Tactics.lean
index 5e95bfc..d5dfd4b 100644
--- a/server/testgame/TestGame/Tactics.lean
+++ b/server/adam/Adam/Tactics.lean
@@ -1,5 +1,5 @@
 import Lean
--- import TestGame.MyNat
+-- import Adam.MyNat
 
 open Lean Elab Tactic
 
diff --git a/server/testgame/TestGame/ToBePorted.lean b/server/adam/Adam/ToBePorted.lean
similarity index 80%
rename from server/testgame/TestGame/ToBePorted.lean
rename to server/adam/Adam/ToBePorted.lean
index 9e01935..7c66039 100644
--- a/server/testgame/TestGame/ToBePorted.lean
+++ b/server/adam/Adam/ToBePorted.lean
@@ -1,5 +1,28 @@
 import Mathlib
 
+open BigOperators
+
+/-! # Delab Problems -/
+
+open Lean PrettyPrinter Delaborator SubExpr
+
+@[delab app.Finset.sum]
+def delabFinsetSum : Delab := do
+  guard $ (← getExpr).getAppNumArgs == 5
+  guard $ ((← getExpr).getArg! 3).isAppOf' ``Finset.univ
+  guard $ ((← getExpr).getArg! 4).isLambda
+  withNaryArg 4 do
+    let α ← withBindingDomain delab
+    withBindingBodyUnusedName fun n => do
+      let n : TSyntax `ident := ⟨n⟩
+      let b ← delab
+      `(∑ $n:ident : $α, $b)
+
+
+
+
+/-! # Other Stuff -/
+
 -- lemma not_odd {n : ℕ} : ¬ Odd n ↔ Even n := by
 --   sorry
 
diff --git a/server/testgame/gameserver b/server/adam/gameserver
similarity index 100%
rename from server/testgame/gameserver
rename to server/adam/gameserver
diff --git a/server/testgame/lake-manifest.json b/server/adam/lake-manifest.json
similarity index 100%
rename from server/testgame/lake-manifest.json
rename to server/adam/lake-manifest.json
diff --git a/server/testgame/lakefile.lean b/server/adam/lakefile.lean
similarity index 85%
rename from server/testgame/lakefile.lean
rename to server/adam/lakefile.lean
index 9ea11dc..d33792a 100644
--- a/server/testgame/lakefile.lean
+++ b/server/adam/lakefile.lean
@@ -6,9 +6,9 @@ require GameServer from ".."/"leanserver"
 require mathlib from git
   "https://github.com/leanprover-community/mathlib4.git"@"master"
 
-package TestGame
+package Adam
 
 @[default_target]
-lean_lib TestGame {
+lean_lib Adam {
   moreLeanArgs := #["-DautoImplicit=false"]
 }
diff --git a/server/testgame/lean-toolchain b/server/adam/lean-toolchain
similarity index 100%
rename from server/testgame/lean-toolchain
rename to server/adam/lean-toolchain
diff --git a/server/build.sh b/server/build.sh
index bc3f11a..21941ea 100644
--- a/server/build.sh
+++ b/server/build.sh
@@ -6,6 +6,16 @@ cd $(dirname $0)
 # Build elan image if not already present
 docker build --pull --rm -f elan.Dockerfile -t elan:latest .
 
-(cd testgame && lake exe cache get && lake build)
-docker rmi testgame:latest || true
-docker build --rm -f server.Dockerfile -t testgame:latest .
+# Build adam
+(cd adam && lake exe cache get && lake build)
+docker rmi adam:latest || true
+docker build \
+  --build-arg GAME_DIR=adam \
+  --rm -f server.Dockerfile -t adam:latest .
+
+# Build NNG
+(cd nng && lake build)
+docker rmi nng:latest || true
+docker build \
+  --build-arg GAME_DIR=nng \
+  --rm -f server.Dockerfile -t nng:latest .
diff --git a/server/index.mjs b/server/index.mjs
index a07dab6..cdb6db9 100644
--- a/server/index.mjs
+++ b/server/index.mjs
@@ -6,6 +6,18 @@ import * as url from 'url';
 import * as rpc from 'vscode-ws-jsonrpc';
 import * as jsonrpcserver from 'vscode-ws-jsonrpc/server';
 
+const games = {
+    adam: {
+        name: "Adam",
+        module: "Adam",
+        queueLength: 5
+    },
+    nng: {
+        name: "NNG",
+        module: "NNG",
+        queueLength: 5
+    }
+}
 
 const __filename = url.fileURLToPath(import.meta.url);
 const __dirname = url.fileURLToPath(new URL('.', import.meta.url));
@@ -23,23 +35,19 @@ const wss = new WebSocketServer({ server })
 const environment = process.env.NODE_ENV
 const isDevelopment = environment === 'development'
 
-let cmd, cmdArgs, cwd;
-if (isDevelopment) {
-    cmd = "./gameserver";
-    cmdArgs = ["--server"];
-    cwd = "./leanserver/build/bin/"
-} else{
-    cmd = "docker";
-    cmdArgs = ["run", "--runtime=runsc", "--network=none", "--rm", "-i", "testgame:latest"];
-    cwd = "."
-}
-
-/** We keep a queue of started Lean Server processes to be ready when a user arrives */
-const queue = []
+/** We keep queues of started Lean Server processes to be ready when a user arrives */
+const queue = {}
 const queueLength = 5
 
-function startServerProcess() {
-    const serverProcess = cp.spawn(cmd, cmdArgs, { cwd })
+function startServerProcess(gameId) {
+    const serverProcess = isDevelopment
+        ? cp.spawn("./gameserver",
+            ["--server", gameId, games[gameId].module, games[gameId].name],
+            { cwd: "./leanserver/build/bin/" })
+        : cp.spawn("docker",
+            ["run", "--runtime=runsc", "--network=none", "--rm", "-i", `${gameId}:latest`,
+              "./gameserver", "--server", gameId, games[gameId].module, games[gameId].name],
+            { cwd: "." })
     serverProcess.on('error', error =>
         console.error(`Launching Lean Server failed: ${error}`)
     );
@@ -52,22 +60,32 @@ function startServerProcess() {
 }
 
 /** start Lean Server processes to refill the queue */
-function fillQueue() {
-    while (queue.length < queueLength) {
-        const serverProcess = startServerProcess()
-        queue.push(serverProcess)
+function fillQueue(gameId) {
+    while (queue[gameId].length < games[gameId].queueLength) {
+        const serverProcess = startServerProcess(gameId)
+        queue[gameId].push(serverProcess)
     }
 }
 
-fillQueue()
+for (let gameId in games) {
+    queue[gameId] = []
+    fillQueue(gameId)
+}
+
+const urlRegEx = new RegExp("^/websocket/(.*)$")
+
+wss.addListener("connection", function(ws, req) {
+    const reRes = urlRegEx.exec(req.url)
+    if (!reRes) { console.error(`Connection refused because of invalid URL: ${req.url}`); return; }
+    const gameId = reRes[1]
+    if (!games[gameId]) { console.error(`Unknown game: ${gameId}`); return; }
 
-wss.addListener("connection", function(ws) {
     let ps;
     if (isDevelopment) { // Don't use queue in development
-        ps = startServerProcess()
+        ps = startServerProcess(gameId)
     } else {
-        ps = queue.shift() // Pick the first Lean process; it's likely to be ready immediately
-        fillQueue()
+        ps = queue[gameId].shift() // Pick the first Lean process; it's likely to be ready immediately
+        fillQueue(gameId)
     }
 
     const socket = {
diff --git a/server/leanserver/GameServer/Commands.lean b/server/leanserver/GameServer/Commands.lean
index fd1044c..65f9cf5 100644
--- a/server/leanserver/GameServer/Commands.lean
+++ b/server/leanserver/GameServer/Commands.lean
@@ -1,7 +1,6 @@
 import Lean
 
 import GameServer.EnvExtensions
-import GameServer.StrInterpolation
 
 open Lean Meta
 
@@ -62,14 +61,44 @@ partial def reprintCore : Syntax → Option Format
 def reprint (stx : Syntax) : Format :=
   reprintCore stx |>.getD ""
 
-syntax hintArg := " (" (&"strict" <|> &"hidden") " := " withoutPosition(term) ")"
+syntax hintArg := atomic(" (" (&"strict" <|> &"hidden") " := " withoutPosition(term) ")")
+
+/-- Remove any spaces at the beginning of a new line -/
+partial def removeIndentation (s : String) : String :=
+  let rec loop (i : String.Pos) (acc : String) (removeSpaces := false) : String :=
+    let c := s.get i
+    let i := s.next i
+    if s.atEnd i then
+      acc.push c
+    else if removeSpaces && c == ' ' then
+      loop i acc (removeSpaces := true)
+    else if c == '\n' then
+      loop i (acc.push c) (removeSpaces := true)
+    else
+      loop i (acc.push c)
+  loop ⟨0⟩ ""
 
 /-- A tactic that can be used inside `Statement`s to indicate in which proof states players should
 see hints. The tactic does not affect the goal state. -/
-elab "Hint" args:hintArg* msg:Lean.Parser.interpolatedStrNoIndent : tactic => do
+elab "Hint" args:hintArg* msg:interpolatedStr(term) : tactic => do
   let mut strict := false
   let mut hidden := false
 
+  -- remove spaces at the beginngng of new lines
+  let msg := TSyntax.mk $ msg.raw.setArgs $ ← msg.raw.getArgs.mapM fun m => do
+    match m with
+    | Syntax.node info k args =>
+      logInfo k
+      if k == interpolatedStrLitKind && args.size == 1 then
+        match args.get! 0 with
+        | (Syntax.atom info' val) =>
+          let val := removeIndentation val
+          return Syntax.node info k #[Syntax.atom info' val]
+        | _ => return m
+      else
+        return m
+    | _ => return m
+
   for arg in args do
     match arg with
     | `(hintArg| (strict := true)) => strict := true
@@ -85,7 +114,7 @@ elab "Hint" args:hintArg* msg:Lean.Parser.interpolatedStrNoIndent : tactic => do
     -- named differently by the player.
     let varsName := `vars
     let text ← withLocalDeclD varsName (mkApp (mkConst ``Array [levelZero]) (mkConst ``Expr)) fun vars => do
-      let mut text ← expandInterpolatedStr ⟨msg.raw⟩ (← `(MessageData)) (← `(toMessageData))
+      let mut text ← `(m! $msg)
       let goalDecl ← goal.getDecl
       let decls := goalDecl.lctx.decls.toArray.filterMap id
       for i in [:decls.size] do
@@ -274,14 +303,21 @@ def checkInventoryDoc (type : InventoryType) (name : Name) : CommandElabM Unit :
 
 /-! ### Tactics -/
 
-/-- Declare a documentation entry for some tactic.
-Expect an identifier and then a string literal. -/
+/-- Documentation entry of a tactic. Example:
+
+```
+TacticDoc rw "`rw` stands for rewrite, etc. "
+```
+
+* The identifier is the tactics name. Some need to be escaped like `«have»`.
+* The description is a string supporting Markdown.
+ -/
 elab "TacticDoc" name:ident content:str : command =>
   modifyEnv (inventoryDocExt.addEntry · {
     category := default
     type := .Tactic
     name := name.getId,
-    userName := name.getId,
+    displayName := name.getId.toString,
     content := content.getString })
 
 /-- Declare tactics that are introduced by this level. -/
@@ -304,14 +340,23 @@ elab "OnlyTactic" args:ident* : command => do
 
 /-! ### Definitions -/
 
-/-- Declare a documentation entry for some definition.
-Expect an identifier and then a string literal. -/
-elab "DefinitionDoc" name:ident content:str : command =>
+/-- Documentation entry of a definition. Example:
+
+```
+DefinitionDoc Function.Bijective as "Bijective" "defined as `Injective f ∧ Surjective`, etc."
+```
+
+* The first identifier is used in the commands `[New/Only/Disabled]Definition`.
+  It is preferably the true name of the definition. However, this is not required.
+* The string following `as` is the displayed name (in the Inventory).
+* The description is a string supporting Markdown.
+ -/
+elab "DefinitionDoc" name:ident "as" displayName:str content:str : command =>
   modifyEnv (inventoryDocExt.addEntry · {
     category := default
     type := .Definition
     name := name.getId,
-    userName := name.getId,
+    displayName := displayName.getString,
     content := content.getString })
 
 /-- Declare definitions that are introduced by this level. -/
@@ -335,15 +380,23 @@ elab "OnlyDefinition" args:ident* : command => do
 
 /-! ### Lemmas -/
 
-/-- Declare a documentation entry for some lemma.
-Expect two identifiers and then a string literal. The first identifier is meant
-as the real name of the lemma while the second is the displayed name. Currently
-the real name isn't used. -/
-elab "LemmaDoc" name:ident "as" userName:ident "in" category:str content:str : command =>
+/-- Documentation entry of a lemma. Example:
+
+```
+LemmaDoc Nat.succ_pos as "succ_pos" in "Nat" "says `0 < n.succ`, etc."
+```
+
+* The first identifier is used in the commands `[New/Only/Disabled]Lemma`.
+  It is preferably the true name of the lemma. However, this is not required.
+* The string following `as` is the displayed name (in the Inventory).
+* The identifier after `in` is the category to group lemmas by (in the Inventory).
+* The description is a string supporting Markdown.
+ -/
+elab "LemmaDoc" name:ident "as" displayName:str "in" category:str content:str : command =>
   modifyEnv (inventoryDocExt.addEntry · {
     name := name.getId,
     type := .Lemma
-    userName := userName.getId,
+    displayName := displayName.getString,
     category := category.getString,
     content := content.getString })
 
@@ -401,9 +454,11 @@ elab "MakeGame" : command => do
     let Availability₀ : HashMap Name ComputedInventoryItem :=
       HashMap.ofList $
         ← allItems.toList.mapM fun name => do
+          let data := (← getInventoryDoc? name inventoryType).get!
           return (name, {
             name
-            category := (← getInventoryDoc? name inventoryType).get!.category
+            displayName := data.displayName
+            category := data.category
             locked := true
             disabled := false})
 
@@ -414,9 +469,11 @@ elab "MakeGame" : command => do
       let predecessors := game.worlds.predecessors worldId
       for predWorldId in predecessors do
         for item in newItemsInWorld.find! predWorldId do
+          let data := (← getInventoryDoc? item inventoryType).get!
           items := items.insert item {
             name := item
-            category := (← getInventoryDoc? item inventoryType).get!.category
+            displayName := data.displayName
+            category := data.category
             locked := false
             disabled := false
           }
@@ -429,13 +486,25 @@ elab "MakeGame" : command => do
 
       for (levelId, level) in levels do
         for item in (level.getInventory inventoryType).new do
-          let category := (← getInventoryDoc? item inventoryType).get!.category
-          items := items.insert item {name := item, category, locked := false, disabled := false}
+          let data := (← getInventoryDoc? item inventoryType).get!
+          items := items.insert item {
+            name := item
+            displayName := data.displayName
+            category := data.category
+            locked := false
+            disabled := false
+          }
 
         let mut disabled : HashSet Name := {}
         for item in (level.getInventory inventoryType).disabled do
-          let category := (← getInventoryDoc? item inventoryType).get!.category
-          items := items.insert item {name := item, category, locked := false, disabled := false}
+          let data := (← getInventoryDoc? item inventoryType).get!
+          items := items.insert item {
+            name := item
+            displayName := data.displayName
+            category := data.category
+            locked := false
+            disabled := false
+          }
           -- (we set disabled to false at first because it applies only to the current level)
           disabled := disabled.insert item
 
diff --git a/server/leanserver/GameServer/EnvExtensions.lean b/server/leanserver/GameServer/EnvExtensions.lean
index 95a2976..e6fd7a0 100644
--- a/server/leanserver/GameServer/EnvExtensions.lean
+++ b/server/leanserver/GameServer/EnvExtensions.lean
@@ -43,7 +43,7 @@ instance : ToString InventoryType := ⟨fun t => match t with
 structure InventoryDocEntry where
   name : Name
   type : InventoryType
-  userName : Name
+  displayName : String
   category : String
   content : String
   deriving ToJson, Repr, Inhabited
@@ -122,6 +122,7 @@ deriving Inhabited
 
 structure ComputedInventoryItem where
   name : Name
+  displayName : String
   category : String
   locked : Bool
   disabled : Bool
diff --git a/server/leanserver/GameServer/FileWorker.lean b/server/leanserver/GameServer/FileWorker.lean
index 3326fa8..9075307 100644
--- a/server/leanserver/GameServer/FileWorker.lean
+++ b/server/leanserver/GameServer/FileWorker.lean
@@ -113,7 +113,7 @@ where addErrorMessage (info : SourceInfo) (s : MessageData) :=
 
 open Elab Meta Expr in
 def compileProof (inputCtx : Parser.InputContext) (snap : Snapshot) (hasWidgets : Bool)
-    (couldBeEndSnap : Bool) (levelParams : Game.DidOpenLevelParams) : IO Snapshot := do
+    (couldBeEndSnap : Bool) (levelParams : Game.DidOpenLevelParams) (initParams : Lsp.InitializeParams): IO Snapshot := do
   -- Recognize end snap
   if inputCtx.input.atEnd snap.mpState.pos ∧ couldBeEndSnap then
     let endSnap : Snapshot := {
@@ -142,7 +142,7 @@ def compileProof (inputCtx : Parser.InputContext) (snap : Snapshot) (hasWidgets
   let (output, _) ← IO.FS.withIsolatedStreams (isolateStderr := server.stderrAsMessages.get snap.cmdState.scopes.head!.opts) <| liftM (m := BaseIO) do
     Elab.Command.catchExceptions
       (getResetInfoTrees *> do
-        let some level ← GameServer.getLevelByFileName? inputCtx.fileName
+        let some level ← GameServer.getLevelByFileName? initParams inputCtx.fileName
           | throwError "Level not found: {inputCtx.fileName}"
         let scope := level.scope
 
@@ -244,7 +244,8 @@ where
     hOut.writeLspNotification { method := "$/game/completed", param }
 
   /-- Elaborates the next command after `parentSnap` and emits diagnostics into `hOut`. -/
-  private def nextSnap (ctx : WorkerContext) (m : DocumentMeta) (cancelTk : CancelToken) (levelParams : Game.DidOpenLevelParams)
+  private def nextSnap (ctx : WorkerContext) (m : DocumentMeta) (cancelTk : CancelToken)
+      (levelParams : Game.DidOpenLevelParams) (initParams : Lsp.InitializeParams)
       : AsyncElabM (Option Snapshot) := do
     cancelTk.check
     let s ← get
@@ -261,7 +262,8 @@ where
     -- Make sure that there is at least one snap after the head snap, so that
     -- we can see the current goal even on an empty document
     let couldBeEndSnap := s.snaps.size > 1
-    let snap ← compileProof m.mkInputContext lastSnap ctx.clientHasWidgets couldBeEndSnap levelParams
+    let snap ← compileProof m.mkInputContext lastSnap ctx.clientHasWidgets couldBeEndSnap
+      levelParams initParams
     set { s with snaps := s.snaps.push snap }
     -- TODO(MH): check for interrupt with increased precision
     cancelTk.check
@@ -299,7 +301,7 @@ where
       publishIleanInfoUpdate m ctx.hOut snaps
       return AsyncList.ofList snaps.toList ++ AsyncList.delayed (← EIO.asTask (ε := ElabTaskError) (prio := .dedicated) do
         IO.sleep startAfterMs
-        AsyncList.unfoldAsync (nextSnap ctx m cancelTk levelParams) { snaps })
+        AsyncList.unfoldAsync (nextSnap ctx m cancelTk levelParams ctx.initParams) { snaps })
 
 end Elab
 
@@ -362,8 +364,9 @@ section Initialization
     fileMap  := default
 
   def compileHeader (m : DocumentMeta) (hOut : FS.Stream) (opts : Options) (hasWidgets : Bool)
-    (levelModule : Name) : IO (Syntax × Task (Except Error (Snapshot × SearchPath))) := do
-    let gameDir := "../../../testgame"
+    (levelModule : Name) (initParams : InitializeParams): IO (Syntax × Task (Except Error (Snapshot × SearchPath))) := do
+    let some gameDir := GameServer.gameDirFromInitParams initParams
+      | throwServerError s!"Invalid rootUri: {initParams.rootUri?}"
 
     -- Determine search paths of the game project by running `lake env printenv LEAN_PATH`.
     let out ← IO.Process.output
@@ -426,7 +429,8 @@ section Initialization
   def initializeWorker (meta : DocumentMeta) (i o e : FS.Stream) (initParams : InitializeParams) (opts : Options)
        (levelParams : Game.DidOpenLevelParams) : IO (WorkerContext × WorkerState) := do
     let clientHasWidgets := initParams.initializationOptions?.bind (·.hasWidgets?) |>.getD false
-    let (headerStx, headerTask) ← compileHeader meta o opts (hasWidgets := clientHasWidgets) levelParams.levelModule
+    let (headerStx, headerTask) ← compileHeader meta o opts (hasWidgets := clientHasWidgets)
+      levelParams.levelModule initParams
     let cancelTk ← CancelToken.new
     let ctx :=
       { hIn  := i
@@ -506,6 +510,7 @@ section MainLoop
     set st
     match msg with
     | Message.request id method (some params) =>
+      if method == "Game.getInteractiveGoals" then throwServerError "HELLO"
       handleRequest id method (toJson params)
       mainLoop levelParams
     | Message.notification "exit" none =>
diff --git a/server/leanserver/GameServer/Game.lean b/server/leanserver/GameServer/Game.lean
index 123269d..4e3681b 100644
--- a/server/leanserver/GameServer/Game.lean
+++ b/server/leanserver/GameServer/Game.lean
@@ -66,6 +66,7 @@ structure DidOpenLevelParams where
 
 structure Doc where
   name: String
+  displayName: String
   text: String
 deriving ToJson
 
@@ -80,11 +81,11 @@ def handleDidOpenLevel (params : Json) : GameServerM Unit := do
   -- Execute the regular handling of the `didOpen` event
   handleDidOpen p
   let fw ← findFileWorker! m.uri
-  let s ← get
+  -- let s ← get
   let c ← read
-  let some lvl ← GameServer.getLevelByFileName? ((System.Uri.fileUriToPath? m.uri).getD m.uri |>.toString)
+  let some lvl ← GameServer.getLevelByFileName? c.initParams ((System.Uri.fileUriToPath? m.uri).getD m.uri |>.toString)
     | do
-      c.hLog.putStr s!"Level not found: {m.uri}"
+      c.hLog.putStr s!"Level not found: {m.uri} {c.initParams.rootUri?}"
       c.hLog.flush
   -- Send an extra notification to the file worker to inform it about the level data
   fw.stdin.writeLspNotification {
@@ -132,7 +133,7 @@ partial def handleServerEvent (ev : ServerEvent) : GameServerM Bool := do
       return true
     | Message.request id "loadDoc" params =>
       let p ← parseParams LoadDocParams (toJson params)
-      let s ← get
+      -- let s ← get
       let c ← read
       let some doc ← getInventoryDoc? p.name p.type
         | do
@@ -140,6 +141,7 @@ partial def handleServerEvent (ev : ServerEvent) : GameServerM Bool := do
             return true
       let doc : Doc :=
           { name := doc.name.toString
+            displayName := doc.displayName
             text := doc.content }
       c.hOut.writeLspResponse ⟨id, ToJson.toJson doc⟩
       return true
diff --git a/server/leanserver/GameServer/RpcHandlers.lean b/server/leanserver/GameServer/RpcHandlers.lean
index 32f3931..78304a5 100644
--- a/server/leanserver/GameServer/RpcHandlers.lean
+++ b/server/leanserver/GameServer/RpcHandlers.lean
@@ -13,15 +13,26 @@ open Meta
 
 namespace GameServer
 
-def levelIdFromFileName? (fileName : String) : Option LevelId := Id.run do
+def splitRootUri (initParams : Lsp.InitializeParams) (i : Nat): Option String := Id.run do
+  let some rootUri := initParams.rootUri?
+    | return none
+  let rootUriParts := rootUri.splitOn "/"
+  if rootUriParts.length == 3 then
+    return rootUriParts[i]?
+  return none
+
+def levelIdFromFileName? (initParams : Lsp.InitializeParams) (fileName : String) : Option LevelId := Id.run do
   let fileParts := fileName.splitOn "/"
   if fileParts.length == 3 then
-    if let some level := fileParts[2]!.toNat? then
-      return some {game := `TestGame, world := fileParts[1]!, level := level}
+    if let (some level, some game) := (fileParts[2]!.toNat?, splitRootUri initParams 2) then
+      return some {game, world := fileParts[1]!, level := level}
   return none
 
-def getLevelByFileName? [Monad m] [MonadEnv m] (fileName : String) : m (Option GameLevel) := do
-  let some levelId := levelIdFromFileName? fileName
+def gameDirFromInitParams (initParams : Lsp.InitializeParams) : Option String :=
+  (splitRootUri initParams 0).map (s!"../../../{·}")
+
+def getLevelByFileName? [Monad m] [MonadEnv m] (initParams : Lsp.InitializeParams) (fileName : String) : m (Option GameLevel) := do
+  let some levelId := levelIdFromFileName? initParams fileName
     | return none
   return ← getLevel? levelId
 
@@ -114,9 +125,9 @@ def evalHintMessage : Expr → MetaM (Array Expr → MessageData) := fun _ => pu
 
 open Meta in
 /-- Find all hints whose trigger matches the current goal -/
-def findHints (goal : MVarId) (doc : FileWorker.EditableDocument) : MetaM (Array GameHint) := do
+def findHints (goal : MVarId) (doc : FileWorker.EditableDocument) (initParams : Lsp.InitializeParams) : MetaM (Array GameHint) := do
   goal.withContext do
-    let some level ← getLevelByFileName? doc.meta.mkInputContext.fileName
+    let some level ← getLevelByFileName? initParams doc.meta.mkInputContext.fileName
       | throwError "Level not found: {doc.meta.mkInputContext.fileName}"
     let hints ← level.hints.filterMapM fun hint => do
       openAbstractCtxResult hint.goal fun hintFVars hintGoal => do
@@ -137,6 +148,7 @@ def findHints (goal : MVarId) (doc : FileWorker.EditableDocument) : MetaM (Array
 open RequestM in
 def getInteractiveGoals (p : Lsp.PlainGoalParams) : RequestM (RequestTask (Option InteractiveGoals)) := do
   let doc ← readDoc
+  let rc ← readThe RequestContext
   let text := doc.meta.text
   let hoverPos := text.lspPosToUtf8Pos p.position
   -- TODO: I couldn't find a good condition to find the correct snap. So we are looking
@@ -152,7 +164,7 @@ def getInteractiveGoals (p : Lsp.PlainGoalParams) : RequestM (RequestTask (Optio
             return List.toArray <| if useAfter then ti.goalsAfter else ti.goalsBefore
           let goals ← ci.runMetaM {} do
              goals.mapM fun goal => do
-              let hints ← findHints goal doc
+              let hints ← findHints goal doc rc.initParams
               return ← goalToInteractive goal hints
           -- compute the goal diff
           -- let goals ← ciAfter.runMetaM {} (do
diff --git a/server/leanserver/GameServer/StrInterpolation.lean b/server/leanserver/GameServer/StrInterpolation.lean
deleted file mode 100644
index db08b36..0000000
--- a/server/leanserver/GameServer/StrInterpolation.lean
+++ /dev/null
@@ -1,149 +0,0 @@
-/- Adapted from `Lean.Parser.StrInterpolation`
-
-This version of interpolated strings deletes any initial spaces from
-new lines. This keeps Markdown from interpreting indented material
-as quotes.
--/
-import Lean
-namespace Lean.Parser
-
-/-- Push `(Syntax.node tk <new-atom>)` onto syntax stack if parse was successful. -/
-def mkNodeTokenNoWs (n : SyntaxNodeKind) (startPos : String.Pos) : ParserFn := fun c s => Id.run do
-  if s.hasError then
-    return s
-  let input     := c.input
-  let stopPos   := s.pos
-  let leading   := mkEmptySubstringAt input startPos
-  let val       := input.extract startPos stopPos
-  let wsStopPos := s.pos
-  let trailing  := { str := input, startPos := stopPos, stopPos := wsStopPos : Substring }
-  let info      := SourceInfo.original leading startPos trailing stopPos
-  s.pushSyntax (Syntax.mkLit n val info)
-
-partial def interpolatedStrNoIndentFn (p : ParserFn) : ParserFn := fun c s =>
-  let input     := c.input
-  let stackSize := s.stackSize
-  let rec parse (startPos : String.Pos) (c : ParserContext) (s : ParserState) : ParserState :=
-    let i     := s.pos
-    if input.atEnd i then
-      let s := s.pushSyntax Syntax.missing
-      let s := s.mkNode interpolatedStrKind stackSize
-      s.setError "unterminated string literal"
-    else
-      let curr := input.get i
-      let s    := s.setPos (input.next i)
-      if curr == '\"' then
-        let s := mkNodeToken interpolatedStrLitKind startPos c s
-        s.mkNode interpolatedStrKind stackSize
-      else if curr == '\n' then
-        -- Ignore initial spaces on a new line
-        let s := mkNodeTokenNoWs interpolatedStrLitKind startPos c s
-        let s := takeWhileFn (fun curr => curr == ' ') c s
-        parse s.pos c s
-      else if curr == '\\' then
-        andthenFn (quotedCharCoreFn isQuotableCharForStrInterpolant) (parse startPos) c s
-      else if curr == '{' then
-        let s := mkNodeToken interpolatedStrLitKind startPos c s
-        let s := p c s
-        if s.hasError then s
-        else
-          let i := s.pos
-          let curr := input.get i
-          if curr == '}' then
-            let s := s.setPos (input.next i)
-            parse i c s
-          else
-            let s := s.pushSyntax Syntax.missing
-            let s := s.mkNode interpolatedStrKind stackSize
-            s.setError "'}'"
-      else
-        parse startPos c s
-  let startPos := s.pos
-  if input.atEnd startPos then
-    s.mkEOIError
-  else
-    let curr  := input.get s.pos;
-    if curr != '\"' then
-      s.mkError "interpolated string"
-    else
-      let s := s.next input startPos
-      parse startPos c s
-
-@[inline] def interpolatedStrNoIndentNoAntiquot (p : Parser) : Parser := {
-  fn   := interpolatedStrNoIndentFn (withoutPosition p).fn,
-  info := mkAtomicInfo "interpolatedStrNoIndent"
-}
-
-def interpolatedStrNoIndent : Parser :=
-  withAntiquot (mkAntiquot "interpolatedStrNoIndent" interpolatedStrKind) $ interpolatedStrNoIndentNoAntiquot termParser
-
-open Lean.PrettyPrinter
-open Lean.PrettyPrinter.Parenthesizer
-open Lean.PrettyPrinter.Formatter
-
-@[combinator_parenthesizer interpolatedStrNoIndent]
-def interpolatedStrNoIndent.parenthesizer := interpolatedStr.parenthesizer
-
-@[combinator_formatter interpolatedStrNoIndent]
-def interpolatedStrNoIndent.formatter := interpolatedStr.formatter
-
-end Lean.Parser
-
-
-/- Adapted from Init/Meta -/
-open Lean
-
-private def decodeInterpStrQuotedChar (s : String) (i : String.Pos) : Option (Char × String.Pos) := do
-  match Syntax.decodeQuotedChar s i with
-  | some r => some r
-  | none   =>
-    let c := s.get i
-    let i := s.next i
-    if c == '{' then pure ('{', i)
-    else none
-
-private partial def decodeInterpStrLit (s : String) : Option String :=
-  let rec loop (i : String.Pos) (acc : String) : Option String :=
-    let c := s.get i
-    let i := s.next i
-    if c == '\"' || c == '{' then
-      pure acc
-    else if c == '\n' then
-      pure (acc.push c)
-    else if s.atEnd i then
-      pure acc
-    else if c == '\\' then do
-      let (c, i) ← decodeInterpStrQuotedChar s i
-      loop i (acc.push c)
-    else
-      loop i (acc.push c)
-  let c := s.get 0
-  if c == '\"' || c == '}' then
-    loop ⟨1⟩ ""
-  else
-    loop ⟨0⟩ ""
-partial def isInterpolatedStrLit? (stx : Syntax) : Option String :=
-  match Syntax.isLit? interpolatedStrLitKind stx with
-  | none     => none
-  | some val => decodeInterpStrLit val
-
-open Elab
-
-def expandInterpolatedStrChunks (chunks : Array Syntax) (mkAppend : Syntax → Syntax → TermElabM Syntax) (mkElem : Syntax → TermElabM Syntax) : TermElabM Syntax := do
-  let mut i := 0
-  let mut result := Syntax.missing
-  for elem in chunks do
-    let elem ← match isInterpolatedStrLit? elem with
-      | none     => mkElem elem
-      | some str => mkElem (Syntax.mkStrLit str)
-    if i == 0 then
-      result := elem
-    else
-      result ← mkAppend result elem
-    i := i+1
-  return result
-
-open TSyntax.Compat in
-def expandInterpolatedStr (interpStr : TSyntax interpolatedStrKind) (type : Term) (toTypeFn : Term) : TermElabM Term := do
-  let r ← expandInterpolatedStrChunks interpStr.raw.getArgs (fun a b => `($a ++ $b)) (fun a => `($toTypeFn $a))
-  `(($r : $type))
diff --git a/server/leanserver/GameServer/Watchdog.lean b/server/leanserver/GameServer/Watchdog.lean
index 039a730..8b6cfca 100644
--- a/server/leanserver/GameServer/Watchdog.lean
+++ b/server/leanserver/GameServer/Watchdog.lean
@@ -1,6 +1,7 @@
 /- This file is mostly copied from `Lean/Server/Watchdog.lean`. -/
 import Lean
 import GameServer.Game
+import Lean.Server.Watchdog
 
 namespace MyServer.Watchdog
 open Lean
@@ -76,9 +77,7 @@ def initAndRunWatchdogAux : GameServerM Unit := do
     catch _ => pure (Message.notification "exit" none)
     | throwServerError "Got `shutdown` request, expected an `exit` notification"
 
-def createEnv : IO Environment := do
-  let gameDir := "../../../testgame"
-
+def createEnv (gameDir : String) (module : String) : IO Environment := do
   -- Determine search paths of the game project by running `lake env printenv LEAN_PATH`.
   let out ← IO.Process.output
     { cwd := gameDir, cmd := "lake", args := #["env","printenv","LEAN_PATH"] }
@@ -93,11 +92,17 @@ def createEnv : IO Environment := do
   -- Set the search path
   Lean.searchPathRef.set paths
 
-  let gameName := `TestGame
-  let env ← importModules [{ module := `Init : Import }, { module := gameName : Import }] {} 0
+  let env ← importModules [{ module := `Init : Import }, { module := module : Import }] {} 0
   return env
 
 def initAndRunWatchdog (args : List String) (i o e : FS.Stream) : IO Unit := do
+  if args.length < 4 then
+    throwServerError s!"Expected 3 command line arguments in addition to `--server`:
+      game directory, the name of the main module, and the name of the game"
+  let gameId := args[1]!
+  let gameDir := s!"../../../{gameId}"
+  let module := args[2]!
+  let gameName := args[3]!
   let workerPath := "./gameserver"
   -- TODO: Do the following commands slow us down?
   let srcSearchPath ← initSrcSearchPath (← getBuildDir)
@@ -106,8 +111,11 @@ def initAndRunWatchdog (args : List String) (i o e : FS.Stream) : IO Unit := do
   let i ← maybeTee "wdIn.txt" false i
   let o ← maybeTee "wdOut.txt" true o
   let e ← maybeTee "wdErr.txt" true e
-  let state := {env := ← createEnv, game := `TestGame}
+  let state := {env := ← createEnv gameDir module, game := gameName}
   let initRequest ← i.readLspRequestAs "initialize" InitializeParams
+  -- We misuse the `rootUri` field to store gameId, module, and gameName
+  let rootUri? := s!"{gameId}/{module}/{gameName}"
+  let initRequest := {initRequest with param := {initRequest.param with rootUri?}}
   o.writeLspResponse {
     id     := initRequest.id
     result := {
diff --git a/server/leanserver/Main.lean b/server/leanserver/Main.lean
index 993172c..39964b7 100644
--- a/server/leanserver/Main.lean
+++ b/server/leanserver/Main.lean
@@ -8,7 +8,7 @@ unsafe def main : List String → IO UInt32 := fun args => do
   Lean.enableInitializersExecution
 
   if args[0]? == some "--server" then
-    MyServer.Watchdog.watchdogMain []
+    MyServer.Watchdog.watchdogMain args
   else if args[0]? == some "--worker" then
     MyServer.FileWorker.workerMain {}
   else
diff --git a/server/nng/NNG.lean b/server/nng/NNG.lean
new file mode 100644
index 0000000..f9dbac0
--- /dev/null
+++ b/server/nng/NNG.lean
@@ -0,0 +1,64 @@
+import GameServer.Commands
+
+import NNG.Levels.Tutorial
+import NNG.Levels.Addition
+import NNG.Levels.Multiplication
+import NNG.Levels.Power
+import NNG.Levels.Function
+import NNG.Levels.Proposition
+import NNG.Levels.AdvProposition
+import NNG.Levels.AdvAddition
+import NNG.Levels.AdvMultiplication
+import NNG.Levels.Inequality
+
+Game "NNG"
+Title "Natural Number Game"
+Introduction
+"
+# Natural Number Game
+
+##### version 2.0.1
+
+Welcome to the natural number game -- a game which shows the power of induction.
+
+In this game, you get own version of the natural numbers, in an interactive
+theorem prover called Lean. Your version of the natural numbers satisfies something called
+the principle of mathematical induction, and a couple of other things too (Peano's axioms).
+Unfortunately, nobody has proved any theorems about these
+natural numbers yet! For example, addition will be defined for you,
+but nobody has proved that `x + y = y + x` yet. This is your job. You're going to
+prove mathematical theorems using the Lean theorem prover. In other words, you're going to solve
+levels in a computer game.
+
+You're going to prove these theorems using *tactics*. The introductory world, Tutorial World,
+will take you through some of these tactics. During your proofs, the assistant shows your
+\"goal\" (i.e. what you're supposed to be proving) and keeps track of the state of your proof.
+
+Click on the blue \"Tutorial World\" to start your journey!
+
+## Save progress
+
+The game stores your progress locally in your browser storage.
+If you delete it, your progress will be lost!
+
+(usually the *website data* gets deleted together with cookies.)
+
+## Credits
+
+* **Content and Lean3-version:** Kevin Buzzard, Mohammad Pedramfar
+* **Game Engine:** Alexander Bentkamp, Jon Eugster, Patrick Massot
+
+## Resources
+
+* The [Lean Zulip chat] forum
+* [Original Lean3 version](https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/)
+* [A textbook-style (lean4) version of the NN-game](https://lovettsoftware.com/NaturalNumbers/TutorialWorld/Level1.lean.html)
+
+"
+
+Path Tutorial → Addition → Function → Proposition → AdvProposition → AdvAddition
+Path AdvAddition → AdvMultiplication → Inequality
+Path Addition → Multiplication → AdvMultiplication
+Path Multiplication → Power
+
+MakeGame
diff --git a/server/nng/NNG/Doc/Definitions.lean b/server/nng/NNG/Doc/Definitions.lean
new file mode 100644
index 0000000..ec56a79
--- /dev/null
+++ b/server/nng/NNG/Doc/Definitions.lean
@@ -0,0 +1,6 @@
+import GameServer.Commands
+
+DefinitionDoc MyNat as "ℕ"
+"
+The Natural Numbers.
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Doc/Lemmas.lean b/server/nng/NNG/Doc/Lemmas.lean
new file mode 100644
index 0000000..f7c4b03
--- /dev/null
+++ b/server/nng/NNG/Doc/Lemmas.lean
@@ -0,0 +1,31 @@
+import GameServer.Commands
+
+LemmaDoc MyNat.add_zero as "add_zero" in "Nat"
+""
+
+LemmaDoc MyNat.add_succ as "add_succ" in "Nat"
+""
+
+LemmaDoc MyNat.zero_add as "zero_add" in "Nat"
+""
+
+LemmaDoc MyNat.add_assoc as "add_assoc" in "Nat"
+""
+
+LemmaDoc MyNat.succ_add as "succ_add" in "Nat"
+""
+
+LemmaDoc MyNat.add_comm as "add_comm" in "Nat"
+""
+
+LemmaDoc MyNat.one_eq_succ_zero as "one_eq_succ_zero" in "Nat"
+""
+
+LemmaDoc not_iff_imp_false as "not_iff_imp_false" in "Prop"
+""
+
+LemmaDoc MyNat.succ_inj as "succ_inj" in "Nat"
+""
+
+LemmaDoc MyNat.zero_ne_succ as "zero_ne_succ" in "Nat"
+""
diff --git a/server/nng/NNG/Doc/Tactics.lean b/server/nng/NNG/Doc/Tactics.lean
new file mode 100644
index 0000000..e0b50a3
--- /dev/null
+++ b/server/nng/NNG/Doc/Tactics.lean
@@ -0,0 +1,57 @@
+import GameServer.Commands
+
+TacticDoc rfl
+"
+"
+
+TacticDoc rewrite
+"
+"
+
+TacticDoc rw
+"
+"
+
+TacticDoc induction
+"
+"
+
+TacticDoc exact
+"
+"
+
+TacticDoc apply
+"
+"
+
+TacticDoc intro
+"
+"
+
+TacticDoc «have»
+"
+"
+
+TacticDoc constructor
+"
+"
+
+TacticDoc rcases
+"
+"
+
+TacticDoc left
+"
+"
+
+TacticDoc right
+"
+"
+
+TacticDoc contradiction
+"
+"
+
+TacticDoc exfalso
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Addition.lean b/server/nng/NNG/Levels/Addition.lean
new file mode 100644
index 0000000..84d3722
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition.lean
@@ -0,0 +1,42 @@
+import NNG.Levels.Addition.Level_1
+import NNG.Levels.Addition.Level_2
+import NNG.Levels.Addition.Level_3
+import NNG.Levels.Addition.Level_4
+import NNG.Levels.Addition.Level_5
+import NNG.Levels.Addition.Level_6
+
+
+Game "NNG"
+World "Addition"
+Title "Addition World"
+
+Introduction
+"
+Welcome to Addition World. If you've done all four levels in tutorial world
+and know about `rewrite` and `rfl`, then you're in the right place. Here's
+a reminder of the things you're now equipped with which we'll need in this world.
+
+## Data:
+
+  * a type called `ℕ` or `MyNat`.
+  * a term `0 : ℕ`, interpreted as the number zero.
+  * a function `succ : ℕ → ℕ`, with `succ n` interpreted as \"the number after `n`\".
+  * Usual numerical notation `0,1,2` etc. (although `2` onwards will be of no use to us until much later ;-) ).
+  * Addition (with notation `a + b`).
+
+## Theorems:
+
+  * `add_zero (a : ℕ) : a + 0 = a`. Use with `rewrite [add_zero]`.
+  * `add_succ (a b : ℕ) : a + succ(b) = succ(a + b)`. Use with `rewrite [add_succ]`.
+  * The principle of mathematical induction. Use with `induction` (which we learn about in this chapter).
+
+
+## Tactics:
+
+  * `rfl` :  proves goals of the form `X = X`.
+  * `rewrite [h]` : if `h` is a proof of `A = B`, changes all `A`'s in the goal to `B`'s.
+  * `induction n with d hd` : we're going to learn this right now.
+
+
+You will also find all this information in your Inventory to read the documentation.
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Addition/Level_1.lean b/server/nng/NNG/Levels/Addition/Level_1.lean
new file mode 100644
index 0000000..e6e849c
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition/Level_1.lean
@@ -0,0 +1,93 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Addition"
+Level 1
+Title "the induction tactic."
+
+open MyNat
+
+set_option tactic.hygienic false
+
+Introduction
+"
+OK so let's see induction in action. We're going to prove
+
+```
+zero_add (n : ℕ) : 0 + n = n
+```
+
+Wait… what is going on here? Didn't we already prove that adding zero to $n$ gave us $n$?
+
+No we didn't! We proved $n + 0 = n$, and that proof was called `add_zero`. We're now
+trying to establish `zero_add`, the proof that $0 + n = n$.
+
+But aren't these two theorems the same?
+
+No they're not! It is *true* that `x + y = y + x`, but we haven't *proved* it yet,
+and in fact we will need both `add_zero` and `zero_add` in order
+to prove this. In fact `x + y = y + x` is the boss level for addition world,
+and `induction` is the only other tactic you'll need to beat it.
+
+Now `add_zero` is one of Peano's axioms, so we don't need to prove it, we already have it.
+To prove `0 + n = n` we need to use induction on $n$. While we're here,
+note that `zero_add` is about zero add something, and `add_zero` is about something add zero.
+The names of the proofs tell you what the theorems are. Anyway, let's prove `0 + n = n`.
+"
+
+Statement zero_add
+"For all natural numbers $n$, we have $0 + n = n$."
+    (n : ℕ) : 0 + n = n := by
+  Hint "You can start a proof by induction over `n` by typing:
+  `induction n with d hd`.
+
+  If you use the `with` part, you can name your variable and induction hypothesis, otherwise
+  they get default names."
+  induction n with n hn
+  · Hint "Now you have two goals. Once you proved the first, you will jump to the second one.
+    This first goal is the base case $n = 0$.
+
+    Recall that you can use all lemmas that are visible in your inventory."
+    Hint (hidden := true) "try using `add_zero`."
+    rw [add_zero]
+    rfl
+  · Hint "Now you jumped to the second goal. Here you have the induction hypothesis
+    `{hn} : 0 + {n} = {n}` and you need to prove the statement for `succ {n}`."
+    Hint (hidden := true) "look at `add_succ`."
+    rw [add_succ]
+    Hint (hidden := true) "At this point you see the term `0 + {n}`, so you can use the
+    induction hypothesis with `rw [{hn}]`."
+    rw [hn]
+    rfl
+
+NewTactic induction
+
+Conclusion
+"
+## Now venture off on your own.
+
+Those three tactics: 
+
+* `induction n with d hd` 
+* `rw [h]`
+* `rfl`
+
+will get you quite a long way through this game. Using only these tactics
+you can beat Addition World level 4 (the boss level of Addition World),
+all of Multiplication World including the boss level `a * b = b * a`,
+and even all of Power World including the fiendish final boss. This route will
+give you a good grounding in these three basic tactics; after that, if you
+are still interested, there are other worlds to master, where you can learn
+more tactics.
+
+But we're getting ahead of ourselves, you still have to beat the rest of Addition World. 
+We're going to stop explaining stuff carefully now. If you get stuck or want
+to know more about Lean (e.g. how to do much harder maths in Lean),
+ask in `#new members` at
+[the Lean chat](https://leanprover.zulipchat.com)
+(login required, real name preferred). Kevin or Mohammad or one of the other
+people there might be able to help.
+
+Good luck! Click on \"Next\" to solve some levels on your own.
+"
diff --git a/server/nng/NNG/Levels/Addition/Level_2.lean b/server/nng/NNG/Levels/Addition/Level_2.lean
new file mode 100644
index 0000000..d89e00f
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition/Level_2.lean
@@ -0,0 +1,72 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Addition"
+Level 2
+Title "add_assoc (associativity of addition)"
+
+open MyNat
+
+namespace AdditionWorld
+
+theorem zero_add (n : ℕ) : 0 + n = n := by
+  induction n with n hn
+  · rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hn]
+    rfl
+
+Introduction
+"
+It's well-known that $(1 + 2) + 3 = 1 + (2 + 3)$; if we have three numbers
+to add up, it doesn't matter which of the additions we do first. This fact
+is called *associativity of addition* by mathematicians, and it is *not*
+obvious. For example, subtraction really is not associative: $(6 - 2) - 1$
+is really not equal to $6 - (2 - 1)$. We are going to have to prove
+that addition, as defined the way we've defined it, is associative.
+
+See if you can prove associativity of addition.
+"
+
+Statement add_assoc
+"On the set of natural numbers, addition is associative.
+In other words, for all natural numbers $a, b$ and $c$, we have
+$ (a + b) + c = a + (b + c). $"
+    (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
+  Hint "Because addition was defined by recursion on the right-most variable,
+  use induction on the right-most variable (try other variables at your peril!).
+
+  Note that when Lean writes `a + b + c`, it means `(a + b) + c`. If it wants to talk
+  about `a + (b + c)` it will put the brackets in explictly."
+  Branch
+    induction a
+    Hint "Good luck with that…"
+    rw [zero_add, zero_add]
+    rfl
+  Branch
+    induction b
+    Hint "Good luck with that…"
+  induction c with c hc
+  Hint (hidden := true) "look at the lemma `add_zero`."
+  rw [add_zero]
+  Hint "`rw [add_zero]` only rewrites one term of the form `… + 0`, so you might to
+  use it multiple times."
+  rw [add_zero]
+  rfl
+  Hint (hidden := true) "`add_succ` might help here."
+  rw [add_succ]
+  rw [add_succ]
+  rw [add_succ]
+  Hint (hidden := true) "Now you can use the induction hypothesis."
+  rw [hc]
+  rfl
+
+
+Conclusion
+"
+
+"
+
+NewLemma MyNat.zero_add
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Addition/Level_3.lean b/server/nng/NNG/Levels/Addition/Level_3.lean
new file mode 100644
index 0000000..06d1fd1
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition/Level_3.lean
@@ -0,0 +1,68 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import NNG.Levels.Addition.Level_2
+
+Game "NNG"
+World "Addition"
+Level 3
+Title "succ_add"
+
+open MyNat
+
+namespace AdditionWorld
+
+theorem add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
+  induction c with c hc
+  · rw [add_zero]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [add_succ]
+    rw [add_succ]
+    rw [hc]
+    rfl
+
+Introduction
+"
+Oh no! On the way to `add_comm`, a wild `succ_add` appears. `succ_add`
+is the proof that `succ(a) + b = succ(a + b)` for `a` and `b` in your
+natural number type. We need to prove this now, because we will need
+to use this result in our proof that `a + b = b + a` in the next level.
+
+NB: think about why computer scientists called this result `succ_add` .
+There is a logic to all the names.
+
+Note that if you want to be more precise about exactly where you want
+to rewrite something like `add_succ` (the proof you already have),
+you can do things like `rw [add_succ (succ a)]` or
+`rw [add_succ (succ a) d]`, telling Lean explicitly what to use for
+the input variables for the function `add_succ`. Indeed, `add_succ`
+is a function: it takes as input two variables `a` and `b` and outputs a proof
+that `a + succ(b) = succ(a + b)`. The tactic `rw [add_succ]` just says to Lean \"guess
+what the variables are\".
+"
+
+Statement succ_add
+"For all natural numbers $a, b$, we have
+$ \\operatorname{succ}(a) + b = \\operatorname{succ}(a + b)$."
+    (a b : ℕ) : succ a + b = succ (a + b)  := by
+  Hint (hidden := true) "You might again want to start by induction
+  on the right-most variable."
+  Branch
+    induction a
+    Hint "Induction on `a` will not work."
+  induction b with d hd
+  · rw [add_zero]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hd]
+    rw [add_succ]
+    rfl
+
+NewLemma MyNat.add_assoc
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Addition/Level_4.lean b/server/nng/NNG/Levels/Addition/Level_4.lean
new file mode 100644
index 0000000..e729fb7
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition/Level_4.lean
@@ -0,0 +1,63 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import NNG.Levels.Addition.Level_3
+
+Game "NNG"
+World "Addition"
+Level 4
+Title "`add_comm` (boss level)"
+
+open MyNat
+
+namespace AdditionWorld
+
+theorem succ_add (a b : ℕ) : succ a + b = succ (a + b)  := by
+  induction b with d hd
+  · rw [add_zero]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hd]
+    rw [add_succ]
+    rfl
+
+Introduction
+"
+[boss battle music]
+
+Look in your inventory to see the proofs you have available.
+These should be enough.
+"
+
+Statement add_comm
+"On the set of natural numbers, addition is commutative.
+In other words, for all natural numbers $a$ and $b$, we have
+$a + b = b + a$."
+    (a b : ℕ) : a + b = b + a := by
+  Branch
+    induction a with d hd
+    · rw [zero_add]
+      rw [add_zero]
+      rfl
+    · rw [succ_add]
+      rw [hd]
+      rw [add_succ]
+      rfl
+  induction b with d hd
+  · rw [zero_add]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hd]
+    rw [succ_add]
+    rfl
+
+NewLemma MyNat.succ_add
+
+Conclusion
+"
+If you got this far -- nice! You're nearly ready to make a choice:
+Multiplication World or Function World. But there are just a couple
+more useful lemmas in Addition World which you should prove first.
+Press on to level 5.
+"
diff --git a/server/nng/NNG/Levels/Addition/Level_5.lean b/server/nng/NNG/Levels/Addition/Level_5.lean
new file mode 100644
index 0000000..9c13070
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition/Level_5.lean
@@ -0,0 +1,55 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import NNG.Levels.Addition.Level_4
+
+Game "NNG"
+World "Addition"
+Level 5
+Title "succ_eq_add_one"
+
+open MyNat
+
+namespace AdditionWorld
+
+theorem add_comm (a b : ℕ) : a + b = b + a := by
+  induction b with d hd
+  · rw [zero_add]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hd]
+    rw [succ_add]
+    rfl
+
+theorem one_eq_succ_zero : (1 : ℕ) = succ 0 := by simp only
+
+NewLemma MyNat.add_comm MyNat.one_eq_succ_zero
+
+Introduction
+"
+I've just added `one_eq_succ_zero` (a proof of $1 = \\operatorname{succ}(0)$)
+to your list of theorems; this is true
+by definition of $1$, but we didn't need it until now.
+
+Levels 5 and 6 are the two last levels in Addition World.
+Level 5 involves the number $1$. When you see a $1$ in your goal,
+you can write `rw [one_eq_succ_zero]` to get back
+to something which only mentions `0`. This is a good move because $0$ is easier for us to
+manipulate than $1$ right now, because we have
+some theorems about $0$ (`zero_add`, `add_zero`), but, other than `1 = succ 0`,
+no theorems at all which mention $1$. Let's prove one now.
+"
+
+Statement succ_eq_add_one
+"For any natural number $n$, we have
+$ \\operatorname{succ}(n) = n+1$ ."
+    (n : ℕ) : succ n = n + 1 := by
+  rw [one_eq_succ_zero]
+  rw [add_succ]
+  rw [add_zero]
+  rfl
+
+Conclusion
+"
+Well done! On to the last level!
+"
diff --git a/server/nng/NNG/Levels/Addition/Level_6.lean b/server/nng/NNG/Levels/Addition/Level_6.lean
new file mode 100644
index 0000000..29658e1
--- /dev/null
+++ b/server/nng/NNG/Levels/Addition/Level_6.lean
@@ -0,0 +1,49 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import NNG.Levels.Addition.Level_5
+
+Game "NNG"
+World "Addition"
+Level 6
+Title "add_right_comm"
+
+open MyNat
+
+namespace AdditionWorld
+
+Introduction
+"
+Lean sometimes writes `a + b + c`. What does it mean? The convention is
+that if there are no brackets displayed in an addition formula, the brackets
+are around the left most `+` (Lean's addition is \"left associative\").
+So the goal in this level is `(a + b) + c = (a + c) + b`. This isn't
+quite `add_assoc` or `add_comm`, it's something you'll have to prove
+by putting these two theorems together.
+
+If you hadn't picked up on this already, `rw [add_assoc]` will
+change `(x + y) + z` to `x + (y + z)`, but to change it back
+you will need `rw [← add_assoc]`. Get the left arrow by typing `\\l`
+then the space bar (note that this is L for left, not a number 1).
+Similarly, if `h : a = b` then `rw [h]` will change `a`'s to `b`'s
+and `rw [← h]` will change `b`'s to `a`'s.
+
+Also, you can be (and will need to be, in this level) more precise
+about where to rewrite theorems. `rw add_comm,` will just find the
+first `? + ?` it sees and swap it around. You can target more specific
+additions like this: `rw add_comm a` will swap around
+additions of the form `a + ?`, and `rw add_comm a b,` will only
+swap additions of the form `a + b`.
+"
+
+Statement add_right_comm
+"For all natural numbers $a, b$ and $c$, we have
+$a + b + c = a + c + b$."
+    (a b c : ℕ) : a + b + c = a + c + b := by
+  rw [add_assoc]
+  rw [add_comm b c]
+  rw [←add_assoc]
+  rfl
+
+Conclusion
+"
+"
diff --git a/server/nng/NNG/Levels/AdvAddition.lean b/server/nng/NNG/Levels/AdvAddition.lean
new file mode 100644
index 0000000..cc2e95d
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition.lean
@@ -0,0 +1,22 @@
+import NNG.Levels.AdvAddition.Level_1
+import NNG.Levels.AdvAddition.Level_2
+import NNG.Levels.AdvAddition.Level_3
+import NNG.Levels.AdvAddition.Level_4
+import NNG.Levels.AdvAddition.Level_5
+import NNG.Levels.AdvAddition.Level_6
+import NNG.Levels.AdvAddition.Level_7
+import NNG.Levels.AdvAddition.Level_8
+import NNG.Levels.AdvAddition.Level_9
+import NNG.Levels.AdvAddition.Level_10
+import NNG.Levels.AdvAddition.Level_11
+import NNG.Levels.AdvAddition.Level_12
+import NNG.Levels.AdvAddition.Level_13
+
+
+Game "NNG"
+World "AdvAddition"
+Title "Advanced Addition World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_1.lean b/server/nng/NNG/Levels/AdvAddition/Level_1.lean
new file mode 100644
index 0000000..ded4dae
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_1.lean
@@ -0,0 +1,30 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+theorem MyNat.succ_inj {a b : ℕ} : succ a = succ b → a = b := by simp only [succ.injEq, imp_self]
+
+theorem MyNat.zero_ne_succ (a : ℕ) : zero ≠ succ a := by simp only [ne_eq, not_false_iff]
+
+Statement succ_inj'
+""
+    {a b : ℕ} (hs : succ a = succ b) :  a = b := by
+    exact succ_inj hs
+
+NewLemma MyNat.succ_inj MyNat.zero_ne_succ
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_10.lean b/server/nng/NNG/Levels/AdvAddition/Level_10.lean
new file mode 100644
index 0000000..f9f01c7
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_10.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 10
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_11.lean b/server/nng/NNG/Levels/AdvAddition/Level_11.lean
new file mode 100644
index 0000000..b4d244e
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_11.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 11
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_12.lean b/server/nng/NNG/Levels/AdvAddition/Level_12.lean
new file mode 100644
index 0000000..ddc0e06
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_12.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 12
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_13.lean b/server/nng/NNG/Levels/AdvAddition/Level_13.lean
new file mode 100644
index 0000000..13250ec
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_13.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 13
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_2.lean b/server/nng/NNG/Levels/AdvAddition/Level_2.lean
new file mode 100644
index 0000000..1d22594
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_2.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_3.lean b/server/nng/NNG/Levels/AdvAddition/Level_3.lean
new file mode 100644
index 0000000..09185a8
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_3.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_4.lean b/server/nng/NNG/Levels/AdvAddition/Level_4.lean
new file mode 100644
index 0000000..6973471
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_4.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_5.lean b/server/nng/NNG/Levels/AdvAddition/Level_5.lean
new file mode 100644
index 0000000..c3b8b6f
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_5.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_6.lean b/server/nng/NNG/Levels/AdvAddition/Level_6.lean
new file mode 100644
index 0000000..72623d1
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_6.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_7.lean b/server/nng/NNG/Levels/AdvAddition/Level_7.lean
new file mode 100644
index 0000000..1ef04a2
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_7.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_8.lean b/server/nng/NNG/Levels/AdvAddition/Level_8.lean
new file mode 100644
index 0000000..09a2200
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_8.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvAddition/Level_9.lean b/server/nng/NNG/Levels/AdvAddition/Level_9.lean
new file mode 100644
index 0000000..6acbb8b
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvAddition/Level_9.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvAddition"
+Level 9
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvMultiplication.lean b/server/nng/NNG/Levels/AdvMultiplication.lean
new file mode 100644
index 0000000..903e3d9
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvMultiplication.lean
@@ -0,0 +1,13 @@
+import NNG.Levels.AdvMultiplication.Level_1
+import NNG.Levels.AdvMultiplication.Level_2
+import NNG.Levels.AdvMultiplication.Level_3
+import NNG.Levels.AdvMultiplication.Level_4
+
+
+Game "NNG"
+World "AdvMultiplication"
+Title "Advanced Multiplication World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/AdvMultiplication/Level_1.lean b/server/nng/NNG/Levels/AdvMultiplication/Level_1.lean
new file mode 100644
index 0000000..bb1d6fc
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvMultiplication/Level_1.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvMultiplication"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvMultiplication/Level_2.lean b/server/nng/NNG/Levels/AdvMultiplication/Level_2.lean
new file mode 100644
index 0000000..f1afe1b
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvMultiplication/Level_2.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvMultiplication"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvMultiplication/Level_3.lean b/server/nng/NNG/Levels/AdvMultiplication/Level_3.lean
new file mode 100644
index 0000000..33413e4
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvMultiplication/Level_3.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvMultiplication"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvMultiplication/Level_4.lean b/server/nng/NNG/Levels/AdvMultiplication/Level_4.lean
new file mode 100644
index 0000000..fa3a204
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvMultiplication/Level_4.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvMultiplication"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition.lean b/server/nng/NNG/Levels/AdvProposition.lean
new file mode 100644
index 0000000..8d38a47
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition.lean
@@ -0,0 +1,19 @@
+import NNG.Levels.AdvProposition.Level_1
+import NNG.Levels.AdvProposition.Level_2
+import NNG.Levels.AdvProposition.Level_3
+import NNG.Levels.AdvProposition.Level_4
+import NNG.Levels.AdvProposition.Level_5
+import NNG.Levels.AdvProposition.Level_6
+import NNG.Levels.AdvProposition.Level_7
+import NNG.Levels.AdvProposition.Level_8
+import NNG.Levels.AdvProposition.Level_9
+import NNG.Levels.AdvProposition.Level_10
+
+
+Game "NNG"
+World "AdvProposition"
+Title "Advanced Proposition World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_1.lean b/server/nng/NNG/Levels/AdvProposition/Level_1.lean
new file mode 100644
index 0000000..10868a8
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_1.lean
@@ -0,0 +1,28 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "AdvProposition"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Prop) (p : P) (q : Q) : P ∧ Q := by
+  constructor
+  exact p
+  exact q
+
+NewTactic constructor
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_10.lean b/server/nng/NNG/Levels/AdvProposition/Level_10.lean
new file mode 100644
index 0000000..1622db4
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_10.lean
@@ -0,0 +1,36 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+
+Game "NNG"
+World "AdvProposition"
+Level 10
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Prop) : (¬ Q → ¬ P) → (P → Q) := by
+  by_cases p : P
+  · by_cases q : Q
+    intro h p' -- cc
+    assumption
+    intro h p'
+    have g : ¬ P := h q
+    contradiction
+  · by_cases q : Q
+    intro h p
+    assumption
+    intro h p
+    contradiction
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_2.lean b/server/nng/NNG/Levels/AdvProposition/Level_2.lean
new file mode 100644
index 0000000..526e47a
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_2.lean
@@ -0,0 +1,33 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+
+Game "NNG"
+World "AdvProposition"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+set_option tactic.hygienic false
+
+Statement and_symm
+""
+    (P Q : Prop) : P ∧ Q → Q ∧ P :=  by
+  intro h
+  rcases h with ⟨p, q⟩
+  constructor
+  exact q
+  exact p
+
+NewTactic rcases
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_3.lean b/server/nng/NNG/Levels/AdvProposition/Level_3.lean
new file mode 100644
index 0000000..76415ec
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_3.lean
@@ -0,0 +1,31 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+
+Game "NNG"
+World "AdvProposition"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement and_trans
+""
+    (P Q R : Prop) : P ∧ Q → Q ∧ R → P ∧ R := by
+  intro hpq
+  intro hqr
+  rcases hpq with ⟨p, q⟩
+  rcases hqr with ⟨q', r⟩
+  constructor
+  assumption
+  assumption
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_4.lean b/server/nng/NNG/Levels/AdvProposition/Level_4.lean
new file mode 100644
index 0000000..023bd22
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_4.lean
@@ -0,0 +1,31 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+
+Game "NNG"
+World "AdvProposition"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement iff_trans
+""
+    (P Q R : Prop) : (P ↔ Q) → (Q ↔ R) → (P ↔ R) := by
+  intro hpq
+  intro hqr
+  rcases hpq with ⟨hpq, hqp⟩
+  rcases hqr with ⟨hqr, hrq⟩
+  constructor
+  exact fun x => hqr (hpq x) -- cc
+  exact fun x => hqp (hrq x) -- cc
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_5.lean b/server/nng/NNG/Levels/AdvProposition/Level_5.lean
new file mode 100644
index 0000000..26224e6
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_5.lean
@@ -0,0 +1,34 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+
+Game "NNG"
+World "AdvProposition"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement iff_trans
+""
+    (P Q R : Prop) : (P ↔ Q) → (Q ↔ R) → (P ↔ R) := by
+  intro hpq hqr
+  constructor
+  intro p
+  apply hqr.1
+  apply hpq.1
+  assumption
+  intro r
+  apply hpq.2
+  apply hqr.2
+  assumption
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_6.lean b/server/nng/NNG/Levels/AdvProposition/Level_6.lean
new file mode 100644
index 0000000..01ee698
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_6.lean
@@ -0,0 +1,31 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+import Mathlib.Tactic.LeftRight
+--import Mathlib.Logic.Basic
+
+Game "NNG"
+World "AdvProposition"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Prop) : Q → (P ∨ Q) := by
+  intro q
+  right
+  assumption
+
+NewTactic left right
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_7.lean b/server/nng/NNG/Levels/AdvProposition/Level_7.lean
new file mode 100644
index 0000000..abff8e3
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_7.lean
@@ -0,0 +1,31 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+import Mathlib.Tactic.LeftRight
+
+Game "NNG"
+World "AdvProposition"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement or_symm
+""
+    (P Q : Prop) : P ∨ Q → Q ∨ P := by
+  intro h
+  rcases h with p | q
+  right
+  exact p
+  left
+  exact q
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_8.lean b/server/nng/NNG/Levels/AdvProposition/Level_8.lean
new file mode 100644
index 0000000..fd235cc
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_8.lean
@@ -0,0 +1,49 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+import Mathlib.Tactic.LeftRight
+
+Game "NNG"
+World "AdvProposition"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement and_or_distrib_left
+""
+    (P Q R : Prop) : P ∧ (Q ∨ R) ↔ (P ∧ Q) ∨ (P ∧ R) := by
+  constructor
+  intro h
+  rcases h with ⟨hp, hqr⟩
+  rcases hqr with q | r
+  left
+  constructor
+  assumption
+  assumption
+  right
+  constructor
+  assumption
+  assumption
+  intro h
+  rcases h with hpq | hpr
+  rcases hpq with ⟨p, q⟩
+  constructor
+  assumption
+  left
+  assumption
+  rcases hpr with ⟨hp, hr⟩
+  constructor
+  assumption
+  right
+  assumption
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/AdvProposition/Level_9.lean b/server/nng/NNG/Levels/AdvProposition/Level_9.lean
new file mode 100644
index 0000000..d04f314
--- /dev/null
+++ b/server/nng/NNG/Levels/AdvProposition/Level_9.lean
@@ -0,0 +1,36 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import Std.Tactic.RCases
+import NNG.MyNat.Theorems.Proposition
+
+
+
+Game "NNG"
+World "AdvProposition"
+Level 9
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement contra
+""
+  (P Q : Prop) : (P ∧ ¬ P) → Q := by
+  intro h
+  rcases h with ⟨p, np ⟩
+  contradiction
+  -- rw [not_iff_imp_false] at np
+  -- exfalso
+  -- apply np
+  -- exact p
+
+NewTactic exfalso contradiction
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function.lean b/server/nng/NNG/Levels/Function.lean
new file mode 100644
index 0000000..5b7a403
--- /dev/null
+++ b/server/nng/NNG/Levels/Function.lean
@@ -0,0 +1,18 @@
+import NNG.Levels.Function.Level_1
+import NNG.Levels.Function.Level_2
+import NNG.Levels.Function.Level_3
+import NNG.Levels.Function.Level_4
+import NNG.Levels.Function.Level_5
+import NNG.Levels.Function.Level_6
+import NNG.Levels.Function.Level_7
+import NNG.Levels.Function.Level_8
+import NNG.Levels.Function.Level_9
+
+
+Game "NNG"
+World "Function"
+Title "Function World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Function/Level_1.lean b/server/nng/NNG/Levels/Function/Level_1.lean
new file mode 100644
index 0000000..18aa81f
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_1.lean
@@ -0,0 +1,27 @@
+import NNG.Metadata
+import NNG.MyNat.Theorems.Addition
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Function"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+"If $P$ is true, and $P\\implies Q$ is also true, then $Q$ is true."
+    (P Q : Prop) (p : P) (h : P → Q) : Q := by
+  exact h p
+
+NewTactic exact
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_2.lean b/server/nng/NNG/Levels/Function/Level_2.lean
new file mode 100644
index 0000000..1e27341
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_2.lean
@@ -0,0 +1,28 @@
+import NNG.Metadata
+import NNG.MyNat.Theorems.Addition
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Function"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : ℕ → ℕ := by
+  intro n
+  exact 3 * n + 2
+
+NewTactic intro
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_3.lean b/server/nng/NNG/Levels/Function/Level_3.lean
new file mode 100644
index 0000000..1dc9c55
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_3.lean
@@ -0,0 +1,31 @@
+import NNG.Metadata
+import NNG.MyNat.Theorems.Addition
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Function"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R S T U: Type) (p : P) (h : P → Q) (i : Q → R) (j : Q → T) (k : S → T) (l : T → U) :
+    U := by
+  have q := h p
+  have t : T := j q
+  have u : U := l t
+  exact u
+
+NewTactic «have»
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_4.lean b/server/nng/NNG/Levels/Function/Level_4.lean
new file mode 100644
index 0000000..ab2a23d
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_4.lean
@@ -0,0 +1,37 @@
+import NNG.Metadata
+import NNG.MyNat.Theorems.Addition
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Function"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R S T U: Type)
+(p : P)
+(h : P → Q)
+(i : Q → R)
+(j : Q → T)
+(k : S → T)
+(l : T → U) : U :=
+by
+  apply l
+  apply j
+  apply h
+  exact p
+
+NewTactic apply
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_5.lean b/server/nng/NNG/Levels/Function/Level_5.lean
new file mode 100644
index 0000000..8f00824
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_5.lean
@@ -0,0 +1,27 @@
+import NNG.Metadata
+import NNG.MyNat.Theorems.Addition
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Function"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Type) : P → (Q → P) := by
+  intro p
+  intro q
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_6.lean b/server/nng/NNG/Levels/Function/Level_6.lean
new file mode 100644
index 0000000..7754306
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_6.lean
@@ -0,0 +1,30 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Function"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R : Type) : (P → (Q → R)) → ((P → Q) → (P → R)) := by
+  intro f
+  intro h
+  intro p
+  have j : Q → R := f p
+  apply j
+  apply h
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_7.lean b/server/nng/NNG/Levels/Function/Level_7.lean
new file mode 100644
index 0000000..6cf284b
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_7.lean
@@ -0,0 +1,29 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Function"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q F : Type) : (P → Q) → ((Q → F) → (P → F)) := by
+  intro f
+  intro h
+  intro p
+  apply h
+  apply f
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_8.lean b/server/nng/NNG/Levels/Function/Level_8.lean
new file mode 100644
index 0000000..f715436
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_8.lean
@@ -0,0 +1,27 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Function"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Type) : (P → Q) → ((Q → Empty) → (P → Empty)) := by
+  intros f h p
+  apply h
+  apply f
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Function/Level_9.lean b/server/nng/NNG/Levels/Function/Level_9.lean
new file mode 100644
index 0000000..f612d41
--- /dev/null
+++ b/server/nng/NNG/Levels/Function/Level_9.lean
@@ -0,0 +1,36 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Function"
+Level 9
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (A B C D E F G H I J K L : Type)
+    (f1 : A → B) (f2 : B → E) (f3 : E → D) (f4 : D → A) (f5 : E → F)
+    (f6 : F → C) (f7 : B → C) (f8 : F → G) (f9 : G → J) (f10 : I → J)
+    (f11 : J → I) (f12 : I → H) (f13 : E → H) (f14 : H → K) (f15 : I → L) : A → L := by
+  intro a
+  apply f15
+  apply f11
+  apply f9
+  apply f8
+  apply f5
+  apply f2
+  apply f1
+  exact a
+
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality.lean b/server/nng/NNG/Levels/Inequality.lean
new file mode 100644
index 0000000..87a1766
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality.lean
@@ -0,0 +1,25 @@
+import NNG.Levels.Inequality.Level_1
+import NNG.Levels.Inequality.Level_2
+import NNG.Levels.Inequality.Level_3
+import NNG.Levels.Inequality.Level_4
+import NNG.Levels.Inequality.Level_5
+import NNG.Levels.Inequality.Level_6
+import NNG.Levels.Inequality.Level_7
+import NNG.Levels.Inequality.Level_8
+import NNG.Levels.Inequality.Level_9
+import NNG.Levels.Inequality.Level_10
+import NNG.Levels.Inequality.Level_11
+import NNG.Levels.Inequality.Level_12
+import NNG.Levels.Inequality.Level_13
+import NNG.Levels.Inequality.Level_14
+import NNG.Levels.Inequality.Level_15
+import NNG.Levels.Inequality.Level_16
+import NNG.Levels.Inequality.Level_17
+
+Game "NNG"
+World "Inequality"
+Title "Inequality World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Inequality/Level_1.lean b/server/nng/NNG/Levels/Inequality/Level_1.lean
new file mode 100644
index 0000000..0995685
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_1.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_10.lean b/server/nng/NNG/Levels/Inequality/Level_10.lean
new file mode 100644
index 0000000..a08569a
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_10.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 10
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_11.lean b/server/nng/NNG/Levels/Inequality/Level_11.lean
new file mode 100644
index 0000000..b141e0f
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_11.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 11
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_12.lean b/server/nng/NNG/Levels/Inequality/Level_12.lean
new file mode 100644
index 0000000..9ef7d0e
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_12.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 12
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_13.lean b/server/nng/NNG/Levels/Inequality/Level_13.lean
new file mode 100644
index 0000000..5308b97
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_13.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 13
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_14.lean b/server/nng/NNG/Levels/Inequality/Level_14.lean
new file mode 100644
index 0000000..4fd5211
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_14.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 14
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_15.lean b/server/nng/NNG/Levels/Inequality/Level_15.lean
new file mode 100644
index 0000000..74ff4aa
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_15.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 15
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_16.lean b/server/nng/NNG/Levels/Inequality/Level_16.lean
new file mode 100644
index 0000000..25d25fc
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_16.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 16
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_17.lean b/server/nng/NNG/Levels/Inequality/Level_17.lean
new file mode 100644
index 0000000..f42a282
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_17.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 17
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_2.lean b/server/nng/NNG/Levels/Inequality/Level_2.lean
new file mode 100644
index 0000000..597f6bd
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_2.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_3.lean b/server/nng/NNG/Levels/Inequality/Level_3.lean
new file mode 100644
index 0000000..21d9865
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_3.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_4.lean b/server/nng/NNG/Levels/Inequality/Level_4.lean
new file mode 100644
index 0000000..788af62
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_4.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_5.lean b/server/nng/NNG/Levels/Inequality/Level_5.lean
new file mode 100644
index 0000000..3cf1b1b
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_5.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_6.lean b/server/nng/NNG/Levels/Inequality/Level_6.lean
new file mode 100644
index 0000000..5b28efe
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_6.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_7.lean b/server/nng/NNG/Levels/Inequality/Level_7.lean
new file mode 100644
index 0000000..bc22434
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_7.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_8.lean b/server/nng/NNG/Levels/Inequality/Level_8.lean
new file mode 100644
index 0000000..8cc9b70
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_8.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Inequality/Level_9.lean b/server/nng/NNG/Levels/Inequality/Level_9.lean
new file mode 100644
index 0000000..4c2afa4
--- /dev/null
+++ b/server/nng/NNG/Levels/Inequality/Level_9.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Inequality"
+Level 9
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication.lean b/server/nng/NNG/Levels/Multiplication.lean
new file mode 100644
index 0000000..4ff6d8c
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication.lean
@@ -0,0 +1,18 @@
+import NNG.Levels.Multiplication.Level_1
+import NNG.Levels.Multiplication.Level_2
+import NNG.Levels.Multiplication.Level_3
+import NNG.Levels.Multiplication.Level_4
+import NNG.Levels.Multiplication.Level_5
+import NNG.Levels.Multiplication.Level_6
+import NNG.Levels.Multiplication.Level_7
+import NNG.Levels.Multiplication.Level_8
+import NNG.Levels.Multiplication.Level_9
+
+
+Game "NNG"
+World "Multiplication"
+Title "Multiplication World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Multiplication/Level_1.lean b/server/nng/NNG/Levels/Multiplication/Level_1.lean
new file mode 100644
index 0000000..c2ad14a
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_1.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_2.lean b/server/nng/NNG/Levels/Multiplication/Level_2.lean
new file mode 100644
index 0000000..502e4f6
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_2.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_3.lean b/server/nng/NNG/Levels/Multiplication/Level_3.lean
new file mode 100644
index 0000000..ca45877
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_3.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_4.lean b/server/nng/NNG/Levels/Multiplication/Level_4.lean
new file mode 100644
index 0000000..e692704
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_4.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_5.lean b/server/nng/NNG/Levels/Multiplication/Level_5.lean
new file mode 100644
index 0000000..01e06dc
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_5.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_6.lean b/server/nng/NNG/Levels/Multiplication/Level_6.lean
new file mode 100644
index 0000000..4eeba03
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_6.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_7.lean b/server/nng/NNG/Levels/Multiplication/Level_7.lean
new file mode 100644
index 0000000..746f3c9
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_7.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_8.lean b/server/nng/NNG/Levels/Multiplication/Level_8.lean
new file mode 100644
index 0000000..369d554
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_8.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Multiplication/Level_9.lean b/server/nng/NNG/Levels/Multiplication/Level_9.lean
new file mode 100644
index 0000000..20fb8eb
--- /dev/null
+++ b/server/nng/NNG/Levels/Multiplication/Level_9.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Multiplication"
+Level 9
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power.lean b/server/nng/NNG/Levels/Power.lean
new file mode 100644
index 0000000..54910cb
--- /dev/null
+++ b/server/nng/NNG/Levels/Power.lean
@@ -0,0 +1,16 @@
+import NNG.Levels.Power.Level_1
+import NNG.Levels.Power.Level_2
+import NNG.Levels.Power.Level_3
+import NNG.Levels.Power.Level_4
+import NNG.Levels.Power.Level_5
+import NNG.Levels.Power.Level_6
+import NNG.Levels.Power.Level_7
+import NNG.Levels.Power.Level_8
+
+Game "NNG"
+World "Power"
+Title "Power World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Power/Level_1.lean b/server/nng/NNG/Levels/Power/Level_1.lean
new file mode 100644
index 0000000..6a9192c
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_1.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_2.lean b/server/nng/NNG/Levels/Power/Level_2.lean
new file mode 100644
index 0000000..fe6698a
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_2.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_3.lean b/server/nng/NNG/Levels/Power/Level_3.lean
new file mode 100644
index 0000000..7cf3d38
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_3.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_4.lean b/server/nng/NNG/Levels/Power/Level_4.lean
new file mode 100644
index 0000000..635fd22
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_4.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_5.lean b/server/nng/NNG/Levels/Power/Level_5.lean
new file mode 100644
index 0000000..e9f6dc0
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_5.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_6.lean b/server/nng/NNG/Levels/Power/Level_6.lean
new file mode 100644
index 0000000..eaf97a0
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_6.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_7.lean b/server/nng/NNG/Levels/Power/Level_7.lean
new file mode 100644
index 0000000..f5b1949
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_7.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Power/Level_8.lean b/server/nng/NNG/Levels/Power/Level_8.lean
new file mode 100644
index 0000000..0240bfd
--- /dev/null
+++ b/server/nng/NNG/Levels/Power/Level_8.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Power"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    : true := by
+  trivial
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition.lean b/server/nng/NNG/Levels/Proposition.lean
new file mode 100644
index 0000000..9dc768a
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition.lean
@@ -0,0 +1,18 @@
+import NNG.Levels.Proposition.Level_1
+import NNG.Levels.Proposition.Level_2
+import NNG.Levels.Proposition.Level_3
+import NNG.Levels.Proposition.Level_4
+import NNG.Levels.Proposition.Level_5
+import NNG.Levels.Proposition.Level_6
+import NNG.Levels.Proposition.Level_7
+import NNG.Levels.Proposition.Level_8
+-- import NNG.Levels.Proposition.Level_9 -- `cc` is not ported
+
+
+Game "NNG"
+World "Proposition"
+Title "Proposition World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Proposition/Level_1.lean b/server/nng/NNG/Levels/Proposition/Level_1.lean
new file mode 100644
index 0000000..179f73a
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_1.lean
@@ -0,0 +1,24 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 1
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Prop) (p : P) (h : P → Q) : Q := by
+exact h p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_2.lean b/server/nng/NNG/Levels/Proposition/Level_2.lean
new file mode 100644
index 0000000..d4165df
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_2.lean
@@ -0,0 +1,25 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 2
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    {P : Prop} : P → P := by
+  intro p
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_3.lean b/server/nng/NNG/Levels/Proposition/Level_3.lean
new file mode 100644
index 0000000..707f571
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_3.lean
@@ -0,0 +1,30 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 3
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R S T U: Prop) (p : P) (h : P → Q) (i : Q → R)
+    (j : Q → T) (k : S → T) (l : T → U) : U := by
+  have q := h p
+  have t := j q
+  have u := l t
+  exact u
+
+DisabledTactic apply
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_4.lean b/server/nng/NNG/Levels/Proposition/Level_4.lean
new file mode 100644
index 0000000..e81b416
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_4.lean
@@ -0,0 +1,30 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 4
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R S T U: Prop) (p : P) (h : P → Q) (i : Q → R)
+    (j : Q → T) (k : S → T) (l : T → U) : U := by
+  apply l
+  apply j
+  apply h
+  exact p
+
+DisabledTactic «have» 
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_5.lean b/server/nng/NNG/Levels/Proposition/Level_5.lean
new file mode 100644
index 0000000..30c6832
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_5.lean
@@ -0,0 +1,26 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 5
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Prop) : P → (Q → P) := by
+  intro p
+  intro q
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_6.lean b/server/nng/NNG/Levels/Proposition/Level_6.lean
new file mode 100644
index 0000000..2d71058
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_6.lean
@@ -0,0 +1,30 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 6
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R : Prop) : (P → (Q → R)) → ((P → Q) → (P → R)) := by
+  intro f
+  intro h
+  intro p
+  have j : Q → R := f p
+  apply j
+  apply h
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_7.lean b/server/nng/NNG/Levels/Proposition/Level_7.lean
new file mode 100644
index 0000000..5caa3a3
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_7.lean
@@ -0,0 +1,28 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Proposition"
+Level 7
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q R : Prop) : (P → Q) → ((Q → R) → (P → R)) := by
+  intro hpq hqr
+  intro p
+  apply hqr
+  apply hpq
+  exact p
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_8.lean b/server/nng/NNG/Levels/Proposition/Level_8.lean
new file mode 100644
index 0000000..566034c
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_8.lean
@@ -0,0 +1,35 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import NNG.MyNat.Theorems.Proposition
+
+
+Game "NNG"
+World "Proposition"
+Level 8
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (P Q : Prop) : (P → Q) → (¬ Q → ¬ P) := by
+  rw [not_iff_imp_false]
+  rw [not_iff_imp_false]
+  intro f
+  intro h
+  intro p
+  apply h
+  apply f
+  exact p
+
+NewLemma not_iff_imp_false
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Proposition/Level_9.lean b/server/nng/NNG/Levels/Proposition/Level_9.lean
new file mode 100644
index 0000000..3f83050
--- /dev/null
+++ b/server/nng/NNG/Levels/Proposition/Level_9.lean
@@ -0,0 +1,29 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+import NNG.MyNat.Theorems.Proposition
+
+Game "NNG"
+World "Proposition"
+Level 9
+Title ""
+
+open MyNat
+
+Introduction
+"
+
+"
+
+Statement
+""
+    (A B C D E F G H I J K L : Prop)
+    (f1 : A → B) (f2 : B → E) (f3 : E → D) (f4 : D → A) (f5 : E → F)
+    (f6 : F → C) (f7 : B → C) (f8 : F → G) (f9 : G → J) (f10 : I → J)
+    (f11 : J → I) (f12 : I → H) (f13 : E → H) (f14 : H → K) (f15 : I → L) : A → L := by
+  -- cc -- TODO: `cc` is not ported yet.
+  sorry
+
+Conclusion
+"
+
+"
diff --git a/server/nng/NNG/Levels/Tutorial.lean b/server/nng/NNG/Levels/Tutorial.lean
new file mode 100644
index 0000000..5fcd9a3
--- /dev/null
+++ b/server/nng/NNG/Levels/Tutorial.lean
@@ -0,0 +1,12 @@
+import NNG.Levels.Tutorial.Level_1
+import NNG.Levels.Tutorial.Level_2
+import NNG.Levels.Tutorial.Level_3
+import NNG.Levels.Tutorial.Level_4
+
+Game "NNG"
+World "Tutorial"
+Title "Tutorial World"
+
+Introduction
+"
+"
\ No newline at end of file
diff --git a/server/nng/NNG/Levels/Tutorial/Level_1.lean b/server/nng/NNG/Levels/Tutorial/Level_1.lean
new file mode 100644
index 0000000..13a6d5b
--- /dev/null
+++ b/server/nng/NNG/Levels/Tutorial/Level_1.lean
@@ -0,0 +1,42 @@
+import NNG.Metadata
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Tutorial"
+Level 1
+Title "The rfl tactic"
+
+Introduction
+"
+Each level in this game involves proving a mathematical statement. In this first level
+you have three natural numbers $x, y, z$ (listed under \"Objects\") and you want to prove
+$x \\cdot y + z = x \\cdot y + z$ (displayed under \"Goal\").
+
+You can modify the Goal using *Tactics* until you can close (i.e. prove) it. 
+
+The first tactic is called `rfl`, which stands for \"reflexivity\",
+a fancy way of saying that it will prove any goal of the form `A = A`. It doesn't matter how
+complicated `A` is, all that matters is that the left hand side is exactly equal to the right hand
+side (a computer scientist would say \"definitionally equal\"). I really mean \"press the same buttons
+on your computer in the same order\" equal. For example, `x * y + z = x * y + z` can be proved by `rfl`,
+but `x + y = y + x` cannot.
+"
+
+Statement
+"For all natural numbers $x, y$ and $z$, we have $xy + z = xy + z$."
+    (x y z : ℕ) : x * y + z = x * y + z := by
+  Hint "In order to use the tactic `rfl` you can enter it above and hit \"Execute\"."
+  rfl
+
+NewTactic rfl
+NewDefinition MyNat
+
+Conclusion
+"
+Congratulations! You completed your first verified proof!
+
+If you want to be reminded about the `rfl` tactic, your inventory on the right contains useful
+information about things you've learned.
+
+Now click on \"Next\" to continue the journey.
+"
diff --git a/server/nng/NNG/Levels/Tutorial/Level_2.lean b/server/nng/NNG/Levels/Tutorial/Level_2.lean
new file mode 100644
index 0000000..a17243e
--- /dev/null
+++ b/server/nng/NNG/Levels/Tutorial/Level_2.lean
@@ -0,0 +1,46 @@
+import NNG.Metadata
+import NNG.MyNat.Multiplication
+
+Game "NNG"
+World "Tutorial"
+Level 2
+Title "the rewrite (rw) tactic"
+
+Introduction
+"
+In this level, you also get \"Assumptions\" about your objects. These are hypotheses of which
+you assume (or know) that they are true.
+
+The `rewrite` tactic is the way to \"substitute in\" the value of a variable.
+If you have a hypothesis of the form `A = B`, and your goal mentions
+the left hand side `A` somewhere,
+then the rewrite tactic will replace the `A` in your goal with a `B`.
+
+*(Note: For this game, `rw` is a shorthand for `rewrite`. Out in the real world, `rw` tries to call
+`rfl` automatically afterwards.)*
+"
+
+Statement
+"If $x$ and $y$ are natural numbers, and $y = x + 7$, then $2y = 2(x + 7)$."
+    (x y : ℕ) (h : y = x + 7) : 2 * y = 2 * (x + 7) := by
+  Hint "You can use `rewrite [h]` to replace the `{y}` with `x + 7`.
+  Note that the assumption `h` is written
+  inside square brackets: `[h]`."
+  rw [h]
+  Hint "In this game not all hints are directly shown. If you need help finishing the proof, click
+  on \"More Help\" below!"
+  Hint (hidden := true)
+  "Now both sides are identical, so you can use `rfl` to close the goal."
+  rfl
+
+NewTactic rewrite rw
+
+Conclusion
+"
+If you want to see the entire proof you created, toggle \"Editor mode\" above.
+
+There you can also move your cursor around the proof to see the \"state\" of the proof at this point.
+
+Each tactic is written on a new line and Lean is sensitive to indentation (i.e. there must be no
+spaces before any of the tactics)
+"
diff --git a/server/nng/NNG/Levels/Tutorial/Level_3.lean b/server/nng/NNG/Levels/Tutorial/Level_3.lean
new file mode 100644
index 0000000..a65e434
--- /dev/null
+++ b/server/nng/NNG/Levels/Tutorial/Level_3.lean
@@ -0,0 +1,71 @@
+import NNG.Metadata
+import NNG.MyNat.Definition
+
+Game "NNG"
+World "Tutorial"
+Level 3
+Title "Peano axioms"
+
+open MyNat
+
+Introduction
+"
+Now we start from the beginning, where we don't know about addition or multiplication on `ℕ`.
+
+All we get is the following data:
+
+* a term `(0 : ℕ)`, interpreted as the zero number.
+* a function `succ : ℕ → ℕ`, with `succ n` interpreted as \"the number after $n$\".
+* the principle of mathematical induction.
+
+These axioms are essentially the axioms isolated by Peano which uniquely characterise the natural
+numbers (we also need recursion, but we can ignore it for now).
+The first axiom says that $0$ is a natural number.
+The second says that there is a $\\operatorname{succ}$ function which eats a number and spits out
+the number after it, so $\\operatorname{succ}(0)=1$, $\\operatorname{succ}(1)=2$ and so on.
+
+Peano's last axiom is the principle of mathematical induction. This is a deeper fact.
+It says that if we have infinitely many true/false statements $P(0)$, $P(1)$, $P(2)$ and so on,
+and if $P(0)$ is true, and if for every natural number $d$ we know that $P(d)$ implies
+$P(\\operatorname{succ}(d))$, then $P(n)$ must be true for every natural number $n$.
+It's like saying that if you have a long line of dominoes, and if you knock the first
+one down, and if you know that if a domino falls down then the one after it will fall
+down too, then you can deduce that all the dominos will fall down. One can also think
+of it as saying that every natural number can be built by starting at $0$ and then applying
+$\\operatorname{succ}$ a finite number of times.
+
+Peano's insights were firstly that these axioms completely characterise the natural numbers,
+and secondly that these axioms alone can be used to build a whole bunch of other structure
+on the natural numbers, for example addition, multiplication and so on.
+
+This game is all about seeing how far these axioms of Peano can take us.
+
+Now let us practise the use of `rewrite` with this new function `succ`:
+"
+
+Statement
+"If $\\operatorname{succ}(a) = b$, then $\\operatorname{succ}(\\operatorname{succ}(a)) = \\operatorname{succ}(a)$."
+    (a b : ℕ) (h : (succ a) = b) : succ (succ a) = succ b := by
+  Hint "You can use `rewrite` and your assumption `{h}` to substitute `succ a` with `b`.
+
+  Notes:
+
+  1) We do not need brackets for function application the way we would write
+  them in mathematics: `succ b` means $\\operatorname\{succ}(b)$.
+  2) If you would want to substitute instead `b` with `succ a`, you can do that
+  writing a small `←` (`\\l`, i.e. backslash + small letter L + space)
+  before `h` like this: `rewrite [← h]`."
+  Branch
+    rewrite [← h]
+    Hint (hidden := true) "Now both sides are identical…"
+  rewrite [h]
+  Hint (hidden := true) "Now both sides are identical…"
+  rfl
+
+Conclusion
+"
+You may also be wondering why we keep writing `succ b` instead of `b + 1`.
+This is because we haven't defined addition yet!
+On the next level, the final level of Tutorial World,
+we will introduce addition, and then we'll be ready to enter Addition World.
+"
diff --git a/server/nng/NNG/Levels/Tutorial/Level_4.lean b/server/nng/NNG/Levels/Tutorial/Level_4.lean
new file mode 100644
index 0000000..742c5ac
--- /dev/null
+++ b/server/nng/NNG/Levels/Tutorial/Level_4.lean
@@ -0,0 +1,68 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+Game "NNG"
+World "Tutorial"
+Level 4
+Title "addition"
+
+open MyNat
+
+Introduction
+"
+Peano defined addition $a + b$ by induction on $b$, or, more precisely, by *recursion* on $b$.
+He first explained how to add $0$ to a number: this is the base case.
+
+* `add_zero (a : ℕ) : a + 0 = a`
+
+We will call this theorem `add_zero`.
+More precisely, `add_zero` is the name of the *proof* of the
+theorem. Note the name of this proof. Mathematicians sometimes call it
+\"Lemma 2.1\" or \"Hypothesis P6\" or something.
+But computer scientists call it `add_zero` because it tells you what the answer to
+\"x add zero\" is. It's a much better name than \"Lemma 2.1\".
+Even better, you can use the `rewrite` tactic
+with `add_zero`. If you ever see `x + 0` in your goal,
+`rewrite [add_zero]` should simplify it to `x`. This is
+because `add_zero` is a proof that `x + 0 = x`
+(more precisely, `add_zero x` is a proof that `x + 0 = x` but
+Lean can figure out the `x` from the context).
+
+Now here's the inductive step. If you know how to add $d$ to $a$, then Peano
+tells you how to add $\\operatorname{succ} (d)$ to $a$. It looks like this:
+
+- `add_succ (a d : ℕ) : a + (succ d) = succ (a + d)`
+
+What's going on here is that we assume `a + d` is already defined, and we define
+`a + (succ d)` to be the number after it.
+Note the name of this proof too: `add_succ` tells you how to add a successor
+to something.
+If you ever see `… + succ …` in your goal, you should be able to use
+`rewrite [add_succ]`, to make progress.
+"
+
+Statement
+"For all natural numbers $a$, we have $a + \\operatorname{succ}(0) = a$."
+    (a : ℕ) : a + succ 0 = succ a := by
+  Hint "You find `{a} + succ …` in the goal, so you can use `rewrite` and `add_succ`
+  to make progress."
+  Hint (hidden := true) "Explicitely, type `rewrite [add_succ]`!"
+  rewrite [add_succ]
+  Hint "Now you see a term of the form `… + 0`, so you can use `add_zero`."
+  Hint (hidden := true) "Explicitely, type `rewrite [add_zero]`!"
+  rewrite [add_zero]
+  Hint (hidden := true) "Finally both sides are identical."
+  rfl
+
+NewLemma MyNat.add_succ MyNat.add_zero
+
+Conclusion
+"
+You have finished tutorial world! If you're happy, let's move onto Addition World,
+and learn about proof by induction.
+
+## Inspection time
+
+If you want to examine the proof, toggle \"Editor mode\" and click somewhere
+inside the proof to see the state at that point!
+"
diff --git a/server/nng/NNG/Metadata.lean b/server/nng/NNG/Metadata.lean
new file mode 100644
index 0000000..faf9e98
--- /dev/null
+++ b/server/nng/NNG/Metadata.lean
@@ -0,0 +1,5 @@
+import GameServer.Commands
+import NNG.Doc.Tactics
+import NNG.Doc.Lemmas
+import NNG.Doc.Definitions
+import NNG.Modifications.Tactics
diff --git a/server/nng/NNG/Modifications/Tactics.lean b/server/nng/NNG/Modifications/Tactics.lean
new file mode 100644
index 0000000..4a488bd
--- /dev/null
+++ b/server/nng/NNG/Modifications/Tactics.lean
@@ -0,0 +1,131 @@
+import Mathlib.Lean.Expr.Basic
+import NNG.MyNat.Addition
+import Lean.Elab.Tactic.Basic
+
+/-!
+# Modified `rw`
+
+Modify `rw` to work like `rewrite`.
+
+This is mainly a copy of the implementation of `rewrite` in Lean core.
+-/
+
+namespace MyNat
+
+open Lean.Meta Lean.Elab.Tactic Lean.Parser.Tactic
+
+/--
+Modified `rw` tactic. For this game, `rw` works exactly like `rewrite`.
+-/
+syntax (name := rewriteSeq) "rw" (config)? rwRuleSeq (location)? : tactic
+
+@[tactic MyNat.rewriteSeq] def evalRewriteSeq : Tactic := fun stx => do
+  let cfg ← elabRewriteConfig stx[1]
+  let loc   := expandOptLocation stx[3]
+  withRWRulesSeq stx[0] stx[2] fun symm term => do
+    withLocation loc
+      (rewriteLocalDecl term symm · cfg)
+      (rewriteTarget term symm cfg)
+      (throwTacticEx `rewrite · "did not find instance of the pattern in the current goal")
+
+/-!
+# Modified `induction` tactic
+
+Modify `induction` tactic to always show `(0 : MyNat)` instead of `MyNat.zero` and
+to support the lean3-style `while` keyword.
+
+This is mainly copied and modified from the mathlib-tactic `induction'`.
+-/
+
+def rec' {P : ℕ → Prop} (zero : P 0)
+    (succ : (n : ℕ) → (n_ih : P n) → P (succ n)) (t : ℕ) : P t := by
+  induction t with
+  | zero => assumption
+  | succ n =>
+    apply succ
+    assumption
+
+end MyNat
+
+namespace Lean.Parser.Tactic
+open Meta Elab Elab.Tactic
+
+open private getAltNumFields in evalCases ElimApp.evalAlts.go in
+def ElimApp.evalNames (elimInfo : ElimInfo) (alts : Array ElimApp.Alt) (withArg : Syntax)
+    (numEqs := 0) (numGeneralized := 0) (toClear : Array FVarId := #[]) :
+    TermElabM (Array MVarId) := do
+  let mut names : List Syntax := withArg[1].getArgs |>.toList
+  let mut subgoals := #[]
+  for { name := altName, mvarId := g, .. } in alts do
+    let numFields ← getAltNumFields elimInfo altName
+    let (altVarNames, names') := names.splitAtD numFields (Unhygienic.run `(_))
+    names := names'
+    let (fvars, g) ← g.introN numFields <| altVarNames.map (getNameOfIdent' ·[0])
+    let some (g, subst) ← Cases.unifyEqs? numEqs g {} | pure ()
+    let (_, g) ← g.introNP numGeneralized
+    let g ← liftM $ toClear.foldlM (·.tryClear) g
+    for fvar in fvars, stx in altVarNames do
+      g.withContext <| (subst.apply <| .fvar fvar).addLocalVarInfoForBinderIdent ⟨stx⟩
+    subgoals := subgoals.push g
+  pure subgoals
+
+open private getElimNameInfo generalizeTargets generalizeVars in evalInduction in
+
+/--
+Modified `induction` tactic for this game.
+
+Usage: `induction n with d hd`.
+
+*(The actual `induction` tactic has a more complex `with`-argument that works differently)*
+-/
+elab (name := _root_.MyNat.induction) "induction " tgts:(casesTarget,+)
+    withArg:((" with " (colGt binderIdent)+)?)
+    : tactic => do
+  let targets ← elabCasesTargets tgts.1.getSepArgs
+  let g :: gs ← getUnsolvedGoals | throwNoGoalsToBeSolved
+  g.withContext do
+    let elimInfo ← getElimInfo `MyNat.rec'
+    let targets ← addImplicitTargets elimInfo targets
+    evalInduction.checkTargets targets
+    let targetFVarIds := targets.map (·.fvarId!)
+    g.withContext do
+      let forbidden ← mkGeneralizationForbiddenSet targets
+      let mut s ← getFVarSetToGeneralize targets forbidden
+      let (fvarIds, g) ← g.revert (← sortFVarIds s.toArray)
+      let result ← withRef tgts <| ElimApp.mkElimApp elimInfo targets (← g.getTag)
+      let elimArgs := result.elimApp.getAppArgs
+      ElimApp.setMotiveArg g elimArgs[elimInfo.motivePos]!.mvarId! targetFVarIds
+      g.assign result.elimApp
+      let subgoals ← ElimApp.evalNames elimInfo result.alts withArg
+        (numGeneralized := fvarIds.size) (toClear := targetFVarIds)
+      setGoals <| (subgoals ++ result.others).toList ++ gs
+
+end Lean.Parser.Tactic
+
+
+/-! # `rfl` tactic
+
+Added `withReducible` to prevent `rfl` proving stuff like `n + 0 = n`.
+-/
+
+namespace MyNat
+
+open Lean Meta Elab Tactic
+
+-- @[match_pattern] def MyNat.rfl {α : Sort u} {a : α} : Eq a a := Eq.refl a
+
+/-- Modified `rfl` tactic.
+
+`rfl` closes goals of the form `A = A`.
+
+Note that teh version for this game is somewhat weaker than the real one. -/
+syntax (name := rfl) "rfl" : tactic
+
+@[tactic MyNat.rfl] def evalRfl : Tactic := fun _ =>
+  liftMetaTactic fun mvarId => do withReducible <| mvarId.refl; pure []
+
+-- @[tactic MyNat.rfl] def evalRfl : Tactic := fun _ =>
+--   liftMetaTactic fun mvarId => do mvarId.refl; pure []
+-- (with_reducible rfl)
+
+end MyNat
diff --git a/server/nng/NNG/MyNat/Addition.lean b/server/nng/NNG/MyNat/Addition.lean
new file mode 100644
index 0000000..9f482f4
--- /dev/null
+++ b/server/nng/NNG/MyNat/Addition.lean
@@ -0,0 +1,23 @@
+import NNG.MyNat.Definition
+
+namespace MyNat
+
+open MyNat
+
+def add : MyNat → MyNat → MyNat
+  | a, 0   => a
+  | a, MyNat.succ b => MyNat.succ (MyNat.add a b)
+
+instance : Add MyNat where
+  add := MyNat.add
+
+/--
+This theorem proves that if you add zero to a MyNat you get back the same number.
+-/
+
+theorem add_zero (a : MyNat) : a + 0 = a := by rfl
+
+/--
+This theorem proves that (a + (d + 1)) = ((a + d) + 1) for a,d in MyNat.
+-/
+theorem add_succ (a d : MyNat) : a + (succ d) = succ (a + d) := by rfl
diff --git a/server/nng/NNG/MyNat/Definition.lean b/server/nng/NNG/MyNat/Definition.lean
new file mode 100644
index 0000000..f567b27
--- /dev/null
+++ b/server/nng/NNG/MyNat/Definition.lean
@@ -0,0 +1,37 @@
+--import Mathlib.Tactic.Basic
+--import Mathlib.Tactic.Cases 
+
+/-- Our copy of the natural numbers called `MyNat`. -/
+inductive MyNat where
+| zero : MyNat
+| succ : MyNat → MyNat
+deriving BEq, DecidableEq, Inhabited
+
+@[inherit_doc]
+notation "ℕ" => MyNat
+-- Note: as long as we do not import `Mathlib.Init.Data.Nat.Notation` this is fine.
+
+namespace MyNat
+
+instance : Inhabited MyNat where
+  default := MyNat.zero
+
+def myNatFromNat (x : Nat) : MyNat :=
+  match x with
+  | Nat.zero   => MyNat.zero
+  | Nat.succ b => MyNat.succ (myNatFromNat b)
+
+def natFromMyNat (x : MyNat) : Nat :=
+  match x with
+  | MyNat.zero   => Nat.zero
+  | MyNat.succ b => Nat.succ (natFromMyNat b)
+
+instance ofNat {n : Nat} : OfNat MyNat n where
+  ofNat := myNatFromNat n
+
+instance : ToString MyNat where
+  toString p := toString (natFromMyNat p)
+
+theorem zero_eq_0 : MyNat.zero = 0 := rfl
+
+def one : MyNat := MyNat.succ 0
diff --git a/server/nng/NNG/MyNat/Inequality.lean b/server/nng/NNG/MyNat/Inequality.lean
new file mode 100644
index 0000000..1fb0956
--- /dev/null
+++ b/server/nng/NNG/MyNat/Inequality.lean
@@ -0,0 +1,28 @@
+import NNG.MyNat.Multiplication
+
+-- this is one of *three* routes to
+-- canonically_ordered_comm_semiring
+
+namespace MyNat
+
+def le (a b : MyNat) :=  ∃ (c : MyNat), b = a + c
+
+-- Another choice is to define it recursively:
+-- | le 0 _
+-- | le (succ a) (succ b) = le ab
+
+-- notation
+instance : LE MyNat := ⟨MyNat.le⟩
+
+theorem le_def' : MyNat.le = (.≤.) := rfl
+
+theorem le_iff_exists_add (a b : MyNat) : a ≤ b ↔ ∃ (c : MyNat), b = a + c := Iff.rfl
+
+def lt_myNat (a b : MyNat) := a ≤ b ∧ ¬ (b ≤ a)
+
+instance : LT MyNat := ⟨lt_myNat⟩
+
+theorem lt :  ∀ (a b : MyNat), a < b ↔ a ≤ b ∧ ¬b ≤ a := fun _ _ => Iff.rfl
+
+
+end MyNat
\ No newline at end of file
diff --git a/server/nng/NNG/MyNat/Multiplication.lean b/server/nng/NNG/MyNat/Multiplication.lean
new file mode 100644
index 0000000..53dd6b3
--- /dev/null
+++ b/server/nng/NNG/MyNat/Multiplication.lean
@@ -0,0 +1,17 @@
+import NNG.MyNat.Addition
+
+namespace MyNat
+
+open MyNat
+
+def mul : MyNat → MyNat → MyNat
+  | _, 0   => 0
+  | a, b + 1 => a + (MyNat.mul a b)
+
+instance : Mul MyNat where
+  mul := MyNat.mul
+
+axiom mul_zero (a : MyNat) : a * 0 = 0
+
+axiom mul_succ (a b : MyNat) : a * (succ b) = a * b + a
+
diff --git a/server/nng/NNG/MyNat/Power.lean b/server/nng/NNG/MyNat/Power.lean
new file mode 100644
index 0000000..a1a0a01
--- /dev/null
+++ b/server/nng/NNG/MyNat/Power.lean
@@ -0,0 +1,21 @@
+import NNG.MyNat.Definition
+namespace MyNat
+open MyNat
+
+def pow : MyNat → MyNat → MyNat
+| _, zero => one
+| m, (succ n) => pow m n * m
+
+instance : Pow MyNat MyNat where
+  pow := pow
+
+-- notation a ^ b := pow a b
+
+example : (1 : MyNat) ^ (1 : MyNat) = 1 := rfl
+
+lemma pow_zero (m : MyNat) : m ^ (0 : MyNat) = 1 := rfl
+
+lemma pow_succ (m n : MyNat) : m ^ (succ n) = m ^ n * m := rfl
+
+end MyNat
+
diff --git a/server/nng/NNG/MyNat/Theorems/Addition.lean b/server/nng/NNG/MyNat/Theorems/Addition.lean
new file mode 100644
index 0000000..0d04f8a
--- /dev/null
+++ b/server/nng/NNG/MyNat/Theorems/Addition.lean
@@ -0,0 +1,46 @@
+import NNG.Metadata
+import NNG.MyNat.Addition
+
+open MyNat
+
+theorem MyNat.zero_add (n : ℕ) : 0 + n = n := by
+  induction n with n hn
+  · rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hn]
+    rfl
+
+theorem MyNat.add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
+  induction c with c hc
+  · rw [add_zero]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [add_succ]
+    rw [add_succ]
+    rw [hc]
+    rfl
+
+theorem MyNat.succ_add (a b : ℕ) : succ a + b = succ (a + b)  := by
+  induction b with d hd
+  · rw [add_zero]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hd]
+    rw [add_succ]
+    rfl
+
+theorem MyNat.add_comm (a b : ℕ) : a + b = b + a := by
+  induction b with d hd
+  · rw [zero_add]
+    rw [add_zero]
+    rfl
+  · rw [add_succ]
+    rw [hd]
+    rw [succ_add]
+    rfl
+
+theorem MyNat.one_eq_succ_zero : (1 : ℕ) = succ 0 := by
+  simp only
diff --git a/server/nng/NNG/MyNat/Theorems/Proposition.lean b/server/nng/NNG/MyNat/Theorems/Proposition.lean
new file mode 100644
index 0000000..9901853
--- /dev/null
+++ b/server/nng/NNG/MyNat/Theorems/Proposition.lean
@@ -0,0 +1 @@
+theorem not_iff_imp_false (P : Prop) : ¬ P ↔ P → false := by simp only
diff --git a/server/nng/build/ir/NNG.c b/server/nng/build/ir/NNG.c
new file mode 100644
index 0000000..1af17f6
--- /dev/null
+++ b/server/nng/build/ir/NNG.c
@@ -0,0 +1,73 @@
+// Lean compiler output
+// Module: NNG
+// Imports: Init GameServer.Commands NNG.Levels.Tutorial NNG.Levels.Addition NNG.Levels.Multiplication NNG.Levels.Power NNG.Levels.Function NNG.Levels.Proposition NNG.Levels.AdvProposition NNG.Levels.AdvAddition NNG.Levels.AdvMultiplication NNG.Levels.Inequality
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_GameServer_Commands(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Tutorial(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvMultiplication(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_GameServer_Commands(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Tutorial(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvMultiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG.c.trace b/server/nng/build/ir/NNG.c.trace
new file mode 100644
index 0000000..813ce6e
--- /dev/null
+++ b/server/nng/build/ir/NNG.c.trace
@@ -0,0 +1 @@
+7356427851528760174
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Doc/Definitions.c b/server/nng/build/ir/NNG/Doc/Definitions.c
new file mode 100644
index 0000000..15f9cb0
--- /dev/null
+++ b/server/nng/build/ir/NNG/Doc/Definitions.c
@@ -0,0 +1,33 @@
+// Lean compiler output
+// Module: NNG.Doc.Definitions
+// Imports: Init GameServer.Commands
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_GameServer_Commands(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Doc_Definitions(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_GameServer_Commands(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Doc/Definitions.c.trace b/server/nng/build/ir/NNG/Doc/Definitions.c.trace
new file mode 100644
index 0000000..a4001fc
--- /dev/null
+++ b/server/nng/build/ir/NNG/Doc/Definitions.c.trace
@@ -0,0 +1 @@
+2922655963706979749
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Doc/Lemmas.c b/server/nng/build/ir/NNG/Doc/Lemmas.c
new file mode 100644
index 0000000..0e18b5c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Doc/Lemmas.c
@@ -0,0 +1,33 @@
+// Lean compiler output
+// Module: NNG.Doc.Lemmas
+// Imports: Init GameServer.Commands
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_GameServer_Commands(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Doc_Lemmas(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_GameServer_Commands(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Doc/Lemmas.c.trace b/server/nng/build/ir/NNG/Doc/Lemmas.c.trace
new file mode 100644
index 0000000..a348b20
--- /dev/null
+++ b/server/nng/build/ir/NNG/Doc/Lemmas.c.trace
@@ -0,0 +1 @@
+16771103639053061509
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Doc/Tactics.c b/server/nng/build/ir/NNG/Doc/Tactics.c
new file mode 100644
index 0000000..896dd48
--- /dev/null
+++ b/server/nng/build/ir/NNG/Doc/Tactics.c
@@ -0,0 +1,33 @@
+// Lean compiler output
+// Module: NNG.Doc.Tactics
+// Imports: Init GameServer.Commands
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_GameServer_Commands(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Doc_Tactics(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_GameServer_Commands(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Doc/Tactics.c.trace b/server/nng/build/ir/NNG/Doc/Tactics.c.trace
new file mode 100644
index 0000000..5a55535
--- /dev/null
+++ b/server/nng/build/ir/NNG/Doc/Tactics.c.trace
@@ -0,0 +1 @@
+5348243054589539109
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition.c b/server/nng/build/ir/NNG/Levels/Addition.c
new file mode 100644
index 0000000..64c5101
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition.c
@@ -0,0 +1,53 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition
+// Imports: Init NNG.Levels.Addition.Level_1 NNG.Levels.Addition.Level_2 NNG.Levels.Addition.Level_3 NNG.Levels.Addition.Level_4 NNG.Levels.Addition.Level_5 NNG.Levels.Addition.Level_6
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__6(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition.c.trace b/server/nng/build/ir/NNG/Levels/Addition.c.trace
new file mode 100644
index 0000000..97256e5
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition.c.trace
@@ -0,0 +1 @@
+2084978910118405033
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_1.c b/server/nng/build/ir/NNG/Levels/Addition/Level_1.c
new file mode 100644
index 0000000..4a48f7a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Addition/Level_1.c.trace
new file mode 100644
index 0000000..09a9b3a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_1.c.trace
@@ -0,0 +1 @@
+5269099431713252405
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_2.c b/server/nng/build/ir/NNG/Levels/Addition/Level_2.c
new file mode 100644
index 0000000..86ebe99
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Addition/Level_2.c.trace
new file mode 100644
index 0000000..14654bc
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_2.c.trace
@@ -0,0 +1 @@
+17690234639472501785
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_3.c b/server/nng/build/ir/NNG/Levels/Addition/Level_3.c
new file mode 100644
index 0000000..857252d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_3.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition NNG.Levels.Addition.Level_2
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__2(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Addition/Level_3.c.trace
new file mode 100644
index 0000000..7d2c4df
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_3.c.trace
@@ -0,0 +1 @@
+18302928042269315295
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_4.c b/server/nng/build/ir/NNG/Levels/Addition/Level_4.c
new file mode 100644
index 0000000..7ec61f1
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_4.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition NNG.Levels.Addition.Level_3
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__3(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Addition/Level_4.c.trace
new file mode 100644
index 0000000..72e6acf
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_4.c.trace
@@ -0,0 +1 @@
+12154535057277385306
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_5.c b/server/nng/build/ir/NNG/Levels/Addition/Level_5.c
new file mode 100644
index 0000000..48b3da7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_5.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition NNG.Levels.Addition.Level_4
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__4(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/Addition/Level_5.c.trace
new file mode 100644
index 0000000..b660c1d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_5.c.trace
@@ -0,0 +1 @@
+9679823460697032654
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_6.c b/server/nng/build/ir/NNG/Levels/Addition/Level_6.c
new file mode 100644
index 0000000..9ae92fa
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_6.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Addition.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition NNG.Levels.Addition.Level_5
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Addition_Level__5(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Addition_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Addition_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Addition/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/Addition/Level_6.c.trace
new file mode 100644
index 0000000..13460c6
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Addition/Level_6.c.trace
@@ -0,0 +1 @@
+17709657049698654137
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition.c b/server/nng/build/ir/NNG/Levels/AdvAddition.c
new file mode 100644
index 0000000..7fb0302
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition.c
@@ -0,0 +1,81 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition
+// Imports: Init NNG.Levels.AdvAddition.Level_1 NNG.Levels.AdvAddition.Level_2 NNG.Levels.AdvAddition.Level_3 NNG.Levels.AdvAddition.Level_4 NNG.Levels.AdvAddition.Level_5 NNG.Levels.AdvAddition.Level_6 NNG.Levels.AdvAddition.Level_7 NNG.Levels.AdvAddition.Level_8 NNG.Levels.AdvAddition.Level_9 NNG.Levels.AdvAddition.Level_10 NNG.Levels.AdvAddition.Level_11 NNG.Levels.AdvAddition.Level_12 NNG.Levels.AdvAddition.Level_13
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__8(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__9(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__10(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__11(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__12(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvAddition_Level__13(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__9(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__10(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__11(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__12(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvAddition_Level__13(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition.c.trace
new file mode 100644
index 0000000..9116234
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition.c.trace
@@ -0,0 +1 @@
+7852774950450280612
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_1.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_1.c
new file mode 100644
index 0000000..28751bf
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_1.c.trace
new file mode 100644
index 0000000..d0094f7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_1.c.trace
@@ -0,0 +1 @@
+9336372057508599589
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_10.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_10.c
new file mode 100644
index 0000000..067a4c0
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_10.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_10
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__10(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_10.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_10.c.trace
new file mode 100644
index 0000000..ed3ffc8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_10.c.trace
@@ -0,0 +1 @@
+4008453200266032081
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_11.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_11.c
new file mode 100644
index 0000000..79c427c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_11.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_11
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__11(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_11.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_11.c.trace
new file mode 100644
index 0000000..5b253cc
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_11.c.trace
@@ -0,0 +1 @@
+10015610238961501552
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_12.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_12.c
new file mode 100644
index 0000000..aa7eb84
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_12.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_12
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__12(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_12.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_12.c.trace
new file mode 100644
index 0000000..15d3040
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_12.c.trace
@@ -0,0 +1 @@
+5389173862524826914
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_13.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_13.c
new file mode 100644
index 0000000..a398c07
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_13.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_13
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__13(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_13.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_13.c.trace
new file mode 100644
index 0000000..3535774
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_13.c.trace
@@ -0,0 +1 @@
+185528048873600791
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_2.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_2.c
new file mode 100644
index 0000000..e92c5f0
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_2.c.trace
new file mode 100644
index 0000000..dfa5b14
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_2.c.trace
@@ -0,0 +1 @@
+3507750203879559481
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_3.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_3.c
new file mode 100644
index 0000000..40d76ae
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_3.c.trace
new file mode 100644
index 0000000..410d78c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_3.c.trace
@@ -0,0 +1 @@
+18314890376638277065
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_4.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_4.c
new file mode 100644
index 0000000..e87ab4f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_4.c.trace
new file mode 100644
index 0000000..16e6312
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_4.c.trace
@@ -0,0 +1 @@
+2092365143561121648
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_5.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_5.c
new file mode 100644
index 0000000..87a21e8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_5.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_5.c.trace
new file mode 100644
index 0000000..ff557f6
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_5.c.trace
@@ -0,0 +1 @@
+17123810049702200014
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_6.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_6.c
new file mode 100644
index 0000000..aa85e28
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_6.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_6.c.trace
new file mode 100644
index 0000000..b56da14
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_6.c.trace
@@ -0,0 +1 @@
+9314509491732931710
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_7.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_7.c
new file mode 100644
index 0000000..e357d7d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_7.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_7.c.trace
new file mode 100644
index 0000000..2d90327
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_7.c.trace
@@ -0,0 +1 @@
+13172030794097753806
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_8.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_8.c
new file mode 100644
index 0000000..8e82ba2
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_8.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_8.c.trace
new file mode 100644
index 0000000..c4f1af7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_8.c.trace
@@ -0,0 +1 @@
+10314181165617171139
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_9.c b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_9.c
new file mode 100644
index 0000000..9f357c3
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_9.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvAddition.Level_9
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvAddition_Level__9(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvAddition/Level_9.c.trace b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_9.c.trace
new file mode 100644
index 0000000..e3e3b96
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvAddition/Level_9.c.trace
@@ -0,0 +1 @@
+8205318715931175597
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication.c b/server/nng/build/ir/NNG/Levels/AdvMultiplication.c
new file mode 100644
index 0000000..fd5d855
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication.c
@@ -0,0 +1,45 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvMultiplication
+// Imports: Init NNG.Levels.AdvMultiplication.Level_1 NNG.Levels.AdvMultiplication.Level_2 NNG.Levels.AdvMultiplication.Level_3 NNG.Levels.AdvMultiplication.Level_4
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvMultiplication_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvMultiplication_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvMultiplication_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvMultiplication_Level__4(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvMultiplication(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvMultiplication_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvMultiplication_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvMultiplication_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvMultiplication_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication.c.trace b/server/nng/build/ir/NNG/Levels/AdvMultiplication.c.trace
new file mode 100644
index 0000000..c00fc7d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication.c.trace
@@ -0,0 +1 @@
+5627580921265871323
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_1.c b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_1.c
new file mode 100644
index 0000000..a93a197
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvMultiplication.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvMultiplication_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_1.c.trace
new file mode 100644
index 0000000..fcd4fe6
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_1.c.trace
@@ -0,0 +1 @@
+5496292641504121726
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_2.c b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_2.c
new file mode 100644
index 0000000..ecd4bc8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvMultiplication.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvMultiplication_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_2.c.trace
new file mode 100644
index 0000000..b982607
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_2.c.trace
@@ -0,0 +1 @@
+3065456568864785697
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_3.c b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_3.c
new file mode 100644
index 0000000..5f8240e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvMultiplication.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvMultiplication_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_3.c.trace
new file mode 100644
index 0000000..63f9ad3
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_3.c.trace
@@ -0,0 +1 @@
+11074674160667156308
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_4.c b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_4.c
new file mode 100644
index 0000000..0de9924
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvMultiplication.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvMultiplication_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_4.c.trace
new file mode 100644
index 0000000..428ebc8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvMultiplication/Level_4.c.trace
@@ -0,0 +1 @@
+5171635906789131558
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition.c b/server/nng/build/ir/NNG/Levels/AdvProposition.c
new file mode 100644
index 0000000..421a740
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition.c
@@ -0,0 +1,69 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition
+// Imports: Init NNG.Levels.AdvProposition.Level_1 NNG.Levels.AdvProposition.Level_2 NNG.Levels.AdvProposition.Level_3 NNG.Levels.AdvProposition.Level_4 NNG.Levels.AdvProposition.Level_5 NNG.Levels.AdvProposition.Level_6 NNG.Levels.AdvProposition.Level_7 NNG.Levels.AdvProposition.Level_8 NNG.Levels.AdvProposition.Level_9 NNG.Levels.AdvProposition.Level_10
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__8(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__9(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_AdvProposition_Level__10(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__9(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_AdvProposition_Level__10(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition.c.trace
new file mode 100644
index 0000000..4e9a102
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition.c.trace
@@ -0,0 +1 @@
+9478676650839776721
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_1.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_1.c
new file mode 100644
index 0000000..b33ea5a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_1.c.trace
new file mode 100644
index 0000000..1fa48a1
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_1.c.trace
@@ -0,0 +1 @@
+13140666477521992594
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_10.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_10.c
new file mode 100644
index 0000000..8083a4c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_10.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_10
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__10(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_10.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_10.c.trace
new file mode 100644
index 0000000..790c7bd
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_10.c.trace
@@ -0,0 +1 @@
+18203712100298108367
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_2.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_2.c
new file mode 100644
index 0000000..306eabe
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_2.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_2.c.trace
new file mode 100644
index 0000000..f2787fb
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_2.c.trace
@@ -0,0 +1 @@
+10022829939796104452
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_3.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_3.c
new file mode 100644
index 0000000..6b62118
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_3.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_3.c.trace
new file mode 100644
index 0000000..9e0f004
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_3.c.trace
@@ -0,0 +1 @@
+1967301918816512059
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_4.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_4.c
new file mode 100644
index 0000000..f7ecc78
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_4.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_4.c.trace
new file mode 100644
index 0000000..c2fe35c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_4.c.trace
@@ -0,0 +1 @@
+16129653996493781623
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_5.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_5.c
new file mode 100644
index 0000000..4b69e18
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_5.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_5.c.trace
new file mode 100644
index 0000000..30bf614
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_5.c.trace
@@ -0,0 +1 @@
+16436512257645906503
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_6.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_6.c
new file mode 100644
index 0000000..51c2aca
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_6.c
@@ -0,0 +1,45 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases Mathlib.Tactic.LeftRight
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+lean_object* initialize_Mathlib_Tactic_LeftRight(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Mathlib_Tactic_LeftRight(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_6.c.trace
new file mode 100644
index 0000000..bf05509
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_6.c.trace
@@ -0,0 +1 @@
+14208111587323885963
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_7.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_7.c
new file mode 100644
index 0000000..23b5137
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_7.c
@@ -0,0 +1,45 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases Mathlib.Tactic.LeftRight
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+lean_object* initialize_Mathlib_Tactic_LeftRight(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Mathlib_Tactic_LeftRight(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_7.c.trace
new file mode 100644
index 0000000..807ca0c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_7.c.trace
@@ -0,0 +1 @@
+8730344058151551457
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_8.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_8.c
new file mode 100644
index 0000000..a24c8f9
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_8.c
@@ -0,0 +1,45 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases Mathlib.Tactic.LeftRight
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+lean_object* initialize_Mathlib_Tactic_LeftRight(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Mathlib_Tactic_LeftRight(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_8.c.trace
new file mode 100644
index 0000000..074308d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_8.c.trace
@@ -0,0 +1 @@
+14257091850430971994
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_9.c b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_9.c
new file mode 100644
index 0000000..9b02e9b
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_9.c
@@ -0,0 +1,45 @@
+// Lean compiler output
+// Module: NNG.Levels.AdvProposition.Level_9
+// Imports: Init NNG.Metadata NNG.MyNat.Addition Std.Tactic.RCases NNG.MyNat.Theorems.Proposition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Std_Tactic_RCases(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Proposition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_AdvProposition_Level__9(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Std_Tactic_RCases(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Proposition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/AdvProposition/Level_9.c.trace b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_9.c.trace
new file mode 100644
index 0000000..34aee37
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/AdvProposition/Level_9.c.trace
@@ -0,0 +1 @@
+14967413771991349992
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function.c b/server/nng/build/ir/NNG/Levels/Function.c
new file mode 100644
index 0000000..1096fb8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function.c
@@ -0,0 +1,65 @@
+// Lean compiler output
+// Module: NNG.Levels.Function
+// Imports: Init NNG.Levels.Function.Level_1 NNG.Levels.Function.Level_2 NNG.Levels.Function.Level_3 NNG.Levels.Function.Level_4 NNG.Levels.Function.Level_5 NNG.Levels.Function.Level_6 NNG.Levels.Function.Level_7 NNG.Levels.Function.Level_8 NNG.Levels.Function.Level_9
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__8(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Function_Level__9(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Function_Level__9(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function.c.trace b/server/nng/build/ir/NNG/Levels/Function.c.trace
new file mode 100644
index 0000000..a011cea
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function.c.trace
@@ -0,0 +1 @@
+4955068752717367929
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_1.c b/server/nng/build/ir/NNG/Levels/Function/Level_1.c
new file mode 100644
index 0000000..60c18c8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_1.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Theorems.Addition NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_1.c.trace
new file mode 100644
index 0000000..3648ee3
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_1.c.trace
@@ -0,0 +1 @@
+11635906400192042058
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_2.c b/server/nng/build/ir/NNG/Levels/Function/Level_2.c
new file mode 100644
index 0000000..b5fd02a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_2.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Theorems.Addition NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_2.c.trace
new file mode 100644
index 0000000..2f74304
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_2.c.trace
@@ -0,0 +1 @@
+5739902419023245944
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_3.c b/server/nng/build/ir/NNG/Levels/Function/Level_3.c
new file mode 100644
index 0000000..5e5c417
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_3.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Theorems.Addition NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_3.c.trace
new file mode 100644
index 0000000..3765006
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_3.c.trace
@@ -0,0 +1 @@
+13295869598671621401
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_4.c b/server/nng/build/ir/NNG/Levels/Function/Level_4.c
new file mode 100644
index 0000000..c9563c7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_4.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Theorems.Addition NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_4.c.trace
new file mode 100644
index 0000000..f73245d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_4.c.trace
@@ -0,0 +1 @@
+2060723493075565450
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_5.c b/server/nng/build/ir/NNG/Levels/Function/Level_5.c
new file mode 100644
index 0000000..73ca291
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_5.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Theorems.Addition NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_5.c.trace
new file mode 100644
index 0000000..348e271
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_5.c.trace
@@ -0,0 +1 @@
+33560334747064612
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_6.c b/server/nng/build/ir/NNG/Levels/Function/Level_6.c
new file mode 100644
index 0000000..8cfe33e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_6.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_6.c.trace
new file mode 100644
index 0000000..4fcc927
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_6.c.trace
@@ -0,0 +1 @@
+11236535691868165392
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_7.c b/server/nng/build/ir/NNG/Levels/Function/Level_7.c
new file mode 100644
index 0000000..fa6a455
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_7.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_7.c.trace
new file mode 100644
index 0000000..81404ca
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_7.c.trace
@@ -0,0 +1 @@
+13833688845280623014
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_8.c b/server/nng/build/ir/NNG/Levels/Function/Level_8.c
new file mode 100644
index 0000000..a7ee1bb
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_8.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_8.c.trace
new file mode 100644
index 0000000..247b254
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_8.c.trace
@@ -0,0 +1 @@
+3072509448285891874
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_9.c b/server/nng/build/ir/NNG/Levels/Function/Level_9.c
new file mode 100644
index 0000000..4a3f731
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_9.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Function.Level_9
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Function_Level__9(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Function/Level_9.c.trace b/server/nng/build/ir/NNG/Levels/Function/Level_9.c.trace
new file mode 100644
index 0000000..a7ade54
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Function/Level_9.c.trace
@@ -0,0 +1 @@
+11794545348629460374
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality.c b/server/nng/build/ir/NNG/Levels/Inequality.c
new file mode 100644
index 0000000..19c9284
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality.c
@@ -0,0 +1,97 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality
+// Imports: Init NNG.Levels.Inequality.Level_1 NNG.Levels.Inequality.Level_2 NNG.Levels.Inequality.Level_3 NNG.Levels.Inequality.Level_4 NNG.Levels.Inequality.Level_5 NNG.Levels.Inequality.Level_6 NNG.Levels.Inequality.Level_7 NNG.Levels.Inequality.Level_8 NNG.Levels.Inequality.Level_9 NNG.Levels.Inequality.Level_10 NNG.Levels.Inequality.Level_11 NNG.Levels.Inequality.Level_12 NNG.Levels.Inequality.Level_13 NNG.Levels.Inequality.Level_14 NNG.Levels.Inequality.Level_15 NNG.Levels.Inequality.Level_16 NNG.Levels.Inequality.Level_17
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__8(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__9(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__10(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__11(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__12(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__13(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__14(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__15(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__16(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Inequality_Level__17(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__9(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__10(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__11(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__12(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__13(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__14(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__15(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__16(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Inequality_Level__17(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality.c.trace b/server/nng/build/ir/NNG/Levels/Inequality.c.trace
new file mode 100644
index 0000000..55184cc
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality.c.trace
@@ -0,0 +1 @@
+9336489098668184658
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_1.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_1.c
new file mode 100644
index 0000000..93799f1
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_1.c.trace
new file mode 100644
index 0000000..b5ffa38
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_1.c.trace
@@ -0,0 +1 @@
+15715418939533793162
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_10.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_10.c
new file mode 100644
index 0000000..32776cd
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_10.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_10
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__10(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_10.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_10.c.trace
new file mode 100644
index 0000000..eb78d47
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_10.c.trace
@@ -0,0 +1 @@
+8366872987603129236
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_11.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_11.c
new file mode 100644
index 0000000..1d41270
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_11.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_11
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__11(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_11.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_11.c.trace
new file mode 100644
index 0000000..3e01f72
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_11.c.trace
@@ -0,0 +1 @@
+9104254495681588724
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_12.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_12.c
new file mode 100644
index 0000000..3b5425a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_12.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_12
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__12(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_12.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_12.c.trace
new file mode 100644
index 0000000..5115864
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_12.c.trace
@@ -0,0 +1 @@
+14766865931000247685
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_13.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_13.c
new file mode 100644
index 0000000..bf62bc0
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_13.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_13
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__13(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_13.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_13.c.trace
new file mode 100644
index 0000000..e9d270e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_13.c.trace
@@ -0,0 +1 @@
+7236720961247687624
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_14.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_14.c
new file mode 100644
index 0000000..a76a602
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_14.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_14
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__14(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_14.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_14.c.trace
new file mode 100644
index 0000000..e65fa47
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_14.c.trace
@@ -0,0 +1 @@
+17080990698887132932
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_15.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_15.c
new file mode 100644
index 0000000..3c9173d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_15.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_15
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__15(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_15.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_15.c.trace
new file mode 100644
index 0000000..9a7cd4e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_15.c.trace
@@ -0,0 +1 @@
+15808132813580510808
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_16.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_16.c
new file mode 100644
index 0000000..068662e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_16.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_16
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__16(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_16.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_16.c.trace
new file mode 100644
index 0000000..65a9805
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_16.c.trace
@@ -0,0 +1 @@
+7637579646193566177
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_17.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_17.c
new file mode 100644
index 0000000..7077e0f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_17.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_17
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__17(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_17.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_17.c.trace
new file mode 100644
index 0000000..1983d9c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_17.c.trace
@@ -0,0 +1 @@
+14135338231934509378
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_2.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_2.c
new file mode 100644
index 0000000..5d37942
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_2.c.trace
new file mode 100644
index 0000000..6ada09d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_2.c.trace
@@ -0,0 +1 @@
+10180719735176429031
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_3.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_3.c
new file mode 100644
index 0000000..3d54808
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_3.c.trace
new file mode 100644
index 0000000..3e40b0c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_3.c.trace
@@ -0,0 +1 @@
+10425666160152371884
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_4.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_4.c
new file mode 100644
index 0000000..0e8a92b
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_4.c.trace
new file mode 100644
index 0000000..8aeaca9
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_4.c.trace
@@ -0,0 +1 @@
+5262542741621948205
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_5.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_5.c
new file mode 100644
index 0000000..d3713ae
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_5.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_5.c.trace
new file mode 100644
index 0000000..e6f0c73
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_5.c.trace
@@ -0,0 +1 @@
+10099871401285119100
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_6.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_6.c
new file mode 100644
index 0000000..0d6d71b
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_6.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_6.c.trace
new file mode 100644
index 0000000..02ff8cd
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_6.c.trace
@@ -0,0 +1 @@
+18291074078086778850
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_7.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_7.c
new file mode 100644
index 0000000..8e416bf
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_7.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_7.c.trace
new file mode 100644
index 0000000..ea65ccd
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_7.c.trace
@@ -0,0 +1 @@
+4948452312372643925
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_8.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_8.c
new file mode 100644
index 0000000..8b59cbd
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_8.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_8.c.trace
new file mode 100644
index 0000000..4675054
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_8.c.trace
@@ -0,0 +1 @@
+8910944482383625099
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_9.c b/server/nng/build/ir/NNG/Levels/Inequality/Level_9.c
new file mode 100644
index 0000000..482d92d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_9.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Inequality.Level_9
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Inequality_Level__9(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Inequality/Level_9.c.trace b/server/nng/build/ir/NNG/Levels/Inequality/Level_9.c.trace
new file mode 100644
index 0000000..3ed8de7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Inequality/Level_9.c.trace
@@ -0,0 +1 @@
+10084756629938233881
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication.c b/server/nng/build/ir/NNG/Levels/Multiplication.c
new file mode 100644
index 0000000..65d0279
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication.c
@@ -0,0 +1,65 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication
+// Imports: Init NNG.Levels.Multiplication.Level_1 NNG.Levels.Multiplication.Level_2 NNG.Levels.Multiplication.Level_3 NNG.Levels.Multiplication.Level_4 NNG.Levels.Multiplication.Level_5 NNG.Levels.Multiplication.Level_6 NNG.Levels.Multiplication.Level_7 NNG.Levels.Multiplication.Level_8 NNG.Levels.Multiplication.Level_9
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__8(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Multiplication_Level__9(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Multiplication_Level__9(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication.c.trace
new file mode 100644
index 0000000..aa0fcb8
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication.c.trace
@@ -0,0 +1 @@
+15100919068659915784
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_1.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_1.c
new file mode 100644
index 0000000..28fe579
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_1.c.trace
new file mode 100644
index 0000000..3ceaf84
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_1.c.trace
@@ -0,0 +1 @@
+2681194911731925232
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_2.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_2.c
new file mode 100644
index 0000000..4944242
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_2.c.trace
new file mode 100644
index 0000000..51a6198
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_2.c.trace
@@ -0,0 +1 @@
+10245843345607907477
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_3.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_3.c
new file mode 100644
index 0000000..a75be3f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_3.c.trace
new file mode 100644
index 0000000..35f0e4e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_3.c.trace
@@ -0,0 +1 @@
+8940547588455067611
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_4.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_4.c
new file mode 100644
index 0000000..ac85175
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_4.c.trace
new file mode 100644
index 0000000..a872f1f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_4.c.trace
@@ -0,0 +1 @@
+14993641720182264605
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_5.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_5.c
new file mode 100644
index 0000000..b5b1608
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_5.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_5.c.trace
new file mode 100644
index 0000000..8105ffd
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_5.c.trace
@@ -0,0 +1 @@
+18175551488241716216
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_6.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_6.c
new file mode 100644
index 0000000..ea41cab
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_6.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_6.c.trace
new file mode 100644
index 0000000..2a12214
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_6.c.trace
@@ -0,0 +1 @@
+14531862140867195758
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_7.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_7.c
new file mode 100644
index 0000000..135c507
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_7.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_7.c.trace
new file mode 100644
index 0000000..ffc70ae
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_7.c.trace
@@ -0,0 +1 @@
+15474257035701176495
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_8.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_8.c
new file mode 100644
index 0000000..0995e5b
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_8.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_8.c.trace
new file mode 100644
index 0000000..5757f7c
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_8.c.trace
@@ -0,0 +1 @@
+3648854208530401287
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_9.c b/server/nng/build/ir/NNG/Levels/Multiplication/Level_9.c
new file mode 100644
index 0000000..3fec2ad
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_9.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Multiplication.Level_9
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Multiplication_Level__9(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Multiplication/Level_9.c.trace b/server/nng/build/ir/NNG/Levels/Multiplication/Level_9.c.trace
new file mode 100644
index 0000000..2b1f5bf
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Multiplication/Level_9.c.trace
@@ -0,0 +1 @@
+4975536308483488989
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power.c b/server/nng/build/ir/NNG/Levels/Power.c
new file mode 100644
index 0000000..bd1a706
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power.c
@@ -0,0 +1,61 @@
+// Lean compiler output
+// Module: NNG.Levels.Power
+// Imports: Init NNG.Levels.Power.Level_1 NNG.Levels.Power.Level_2 NNG.Levels.Power.Level_3 NNG.Levels.Power.Level_4 NNG.Levels.Power.Level_5 NNG.Levels.Power.Level_6 NNG.Levels.Power.Level_7 NNG.Levels.Power.Level_8
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Power_Level__8(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Power_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power.c.trace b/server/nng/build/ir/NNG/Levels/Power.c.trace
new file mode 100644
index 0000000..30f497d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power.c.trace
@@ -0,0 +1 @@
+12255441869344750286
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_1.c b/server/nng/build/ir/NNG/Levels/Power/Level_1.c
new file mode 100644
index 0000000..ef1b1c9
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_1.c.trace
new file mode 100644
index 0000000..1d06499
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_1.c.trace
@@ -0,0 +1 @@
+3557218418934706832
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_2.c b/server/nng/build/ir/NNG/Levels/Power/Level_2.c
new file mode 100644
index 0000000..9079e5b
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_2.c.trace
new file mode 100644
index 0000000..f8ba540
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_2.c.trace
@@ -0,0 +1 @@
+3161955687484215514
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_3.c b/server/nng/build/ir/NNG/Levels/Power/Level_3.c
new file mode 100644
index 0000000..20b2663
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_3.c.trace
new file mode 100644
index 0000000..e72a579
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_3.c.trace
@@ -0,0 +1 @@
+13739636179189224786
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_4.c b/server/nng/build/ir/NNG/Levels/Power/Level_4.c
new file mode 100644
index 0000000..bfe83ea
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_4.c.trace
new file mode 100644
index 0000000..9672833
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_4.c.trace
@@ -0,0 +1 @@
+2643256504804179665
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_5.c b/server/nng/build/ir/NNG/Levels/Power/Level_5.c
new file mode 100644
index 0000000..76575a7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_5.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_5.c.trace
new file mode 100644
index 0000000..b91249f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_5.c.trace
@@ -0,0 +1 @@
+14401556251889401930
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_6.c b/server/nng/build/ir/NNG/Levels/Power/Level_6.c
new file mode 100644
index 0000000..b3f3fd1
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_6.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_6.c.trace
new file mode 100644
index 0000000..83f1ba1
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_6.c.trace
@@ -0,0 +1 @@
+16899530818829903575
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_7.c b/server/nng/build/ir/NNG/Levels/Power/Level_7.c
new file mode 100644
index 0000000..c8b95d0
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_7.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_7.c.trace
new file mode 100644
index 0000000..36ca048
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_7.c.trace
@@ -0,0 +1 @@
+8728766979918631633
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_8.c b/server/nng/build/ir/NNG/Levels/Power/Level_8.c
new file mode 100644
index 0000000..aa403b9
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_8.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Power.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Power_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Power/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/Power/Level_8.c.trace
new file mode 100644
index 0000000..83efa59
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Power/Level_8.c.trace
@@ -0,0 +1 @@
+16000363894567288792
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition.c b/server/nng/build/ir/NNG/Levels/Proposition.c
new file mode 100644
index 0000000..f31e1eb
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition.c
@@ -0,0 +1,61 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition
+// Imports: Init NNG.Levels.Proposition.Level_1 NNG.Levels.Proposition.Level_2 NNG.Levels.Proposition.Level_3 NNG.Levels.Proposition.Level_4 NNG.Levels.Proposition.Level_5 NNG.Levels.Proposition.Level_6 NNG.Levels.Proposition.Level_7 NNG.Levels.Proposition.Level_8
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__4(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__5(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__6(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__7(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Proposition_Level__8(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__5(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__6(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__7(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Proposition_Level__8(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition.c.trace b/server/nng/build/ir/NNG/Levels/Proposition.c.trace
new file mode 100644
index 0000000..91cc1cc
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition.c.trace
@@ -0,0 +1 @@
+8034725322126254406
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_1.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_1.c
new file mode 100644
index 0000000..5da8568
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_1.c.trace
new file mode 100644
index 0000000..71d00c7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_1.c.trace
@@ -0,0 +1 @@
+18179347340463669579
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_2.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_2.c
new file mode 100644
index 0000000..23ab12d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_2.c.trace
new file mode 100644
index 0000000..9622df1
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_2.c.trace
@@ -0,0 +1 @@
+13217430201083326791
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_3.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_3.c
new file mode 100644
index 0000000..6ac78d7
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_3.c.trace
new file mode 100644
index 0000000..32f55cb
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_3.c.trace
@@ -0,0 +1 @@
+5299063203734346172
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_4.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_4.c
new file mode 100644
index 0000000..ce268b9
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_4.c.trace
new file mode 100644
index 0000000..619fbad
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_4.c.trace
@@ -0,0 +1 @@
+7415905544244480042
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_5.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_5.c
new file mode 100644
index 0000000..b4b1602
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_5.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_5
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__5(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_5.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_5.c.trace
new file mode 100644
index 0000000..067710f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_5.c.trace
@@ -0,0 +1 @@
+10613228186954229021
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_6.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_6.c
new file mode 100644
index 0000000..456f58a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_6.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_6
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__6(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_6.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_6.c.trace
new file mode 100644
index 0000000..a0c149e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_6.c.trace
@@ -0,0 +1 @@
+7894357058058824740
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_7.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_7.c
new file mode 100644
index 0000000..8281a79
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_7.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_7
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__7(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_7.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_7.c.trace
new file mode 100644
index 0000000..f619780
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_7.c.trace
@@ -0,0 +1 @@
+16656846323211551510
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_8.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_8.c
new file mode 100644
index 0000000..350ff4d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_8.c
@@ -0,0 +1,41 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_8
+// Imports: Init NNG.Metadata NNG.MyNat.Addition NNG.MyNat.Theorems.Proposition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Theorems_Proposition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__8(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Theorems_Proposition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_8.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_8.c.trace
new file mode 100644
index 0000000..ba8e72d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_8.c.trace
@@ -0,0 +1 @@
+13601220282574937828
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_9.c b/server/nng/build/ir/NNG/Levels/Proposition/Level_9.c
new file mode 100644
index 0000000..11f600f
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_9.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Proposition.Level_9
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Proposition_Level__9(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Proposition/Level_9.c.trace b/server/nng/build/ir/NNG/Levels/Proposition/Level_9.c.trace
new file mode 100644
index 0000000..4a5bc97
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Proposition/Level_9.c.trace
@@ -0,0 +1 @@
+15399361750882572321
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial.c b/server/nng/build/ir/NNG/Levels/Tutorial.c
new file mode 100644
index 0000000..a24d933
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial.c
@@ -0,0 +1,45 @@
+// Lean compiler output
+// Module: NNG.Levels.Tutorial
+// Imports: Init NNG.Levels.Tutorial.Level_1 NNG.Levels.Tutorial.Level_2 NNG.Levels.Tutorial.Level_3 NNG.Levels.Tutorial.Level_4
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Tutorial_Level__1(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Tutorial_Level__2(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Tutorial_Level__3(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Levels_Tutorial_Level__4(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Tutorial(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Tutorial_Level__1(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Tutorial_Level__2(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Tutorial_Level__3(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Levels_Tutorial_Level__4(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial.c.trace b/server/nng/build/ir/NNG/Levels/Tutorial.c.trace
new file mode 100644
index 0000000..f666963
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial.c.trace
@@ -0,0 +1 @@
+1595615440839641244
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_1.c b/server/nng/build/ir/NNG/Levels/Tutorial/Level_1.c
new file mode 100644
index 0000000..ae6752a
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_1.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Tutorial.Level_1
+// Imports: Init NNG.Metadata NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Tutorial_Level__1(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_1.c.trace b/server/nng/build/ir/NNG/Levels/Tutorial/Level_1.c.trace
new file mode 100644
index 0000000..029fdab
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_1.c.trace
@@ -0,0 +1 @@
+17057151196775041350
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_2.c b/server/nng/build/ir/NNG/Levels/Tutorial/Level_2.c
new file mode 100644
index 0000000..6244a6e
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_2.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Tutorial.Level_2
+// Imports: Init NNG.Metadata NNG.MyNat.Multiplication
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Tutorial_Level__2(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Multiplication(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_2.c.trace b/server/nng/build/ir/NNG/Levels/Tutorial/Level_2.c.trace
new file mode 100644
index 0000000..f0c7b10
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_2.c.trace
@@ -0,0 +1 @@
+2087975388406110178
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_3.c b/server/nng/build/ir/NNG/Levels/Tutorial/Level_3.c
new file mode 100644
index 0000000..455b9b0
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_3.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Tutorial.Level_3
+// Imports: Init NNG.Metadata NNG.MyNat.Definition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Definition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Tutorial_Level__3(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Definition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_3.c.trace b/server/nng/build/ir/NNG/Levels/Tutorial/Level_3.c.trace
new file mode 100644
index 0000000..4568320
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_3.c.trace
@@ -0,0 +1 @@
+2143617200443064964
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_4.c b/server/nng/build/ir/NNG/Levels/Tutorial/Level_4.c
new file mode 100644
index 0000000..6d85b72
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_4.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.Levels.Tutorial.Level_4
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Levels_Tutorial_Level__4(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Levels/Tutorial/Level_4.c.trace b/server/nng/build/ir/NNG/Levels/Tutorial/Level_4.c.trace
new file mode 100644
index 0000000..03fc4ca
--- /dev/null
+++ b/server/nng/build/ir/NNG/Levels/Tutorial/Level_4.c.trace
@@ -0,0 +1 @@
+7407492338022565581
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Metadata.c b/server/nng/build/ir/NNG/Metadata.c
new file mode 100644
index 0000000..364d1ee
--- /dev/null
+++ b/server/nng/build/ir/NNG/Metadata.c
@@ -0,0 +1,49 @@
+// Lean compiler output
+// Module: NNG.Metadata
+// Imports: Init GameServer.Commands NNG.Doc.Tactics NNG.Doc.Lemmas NNG.Doc.Definitions NNG.Modifications.Tactics
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_GameServer_Commands(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Doc_Tactics(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Doc_Lemmas(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Doc_Definitions(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Modifications_Tactics(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_GameServer_Commands(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Doc_Tactics(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Doc_Lemmas(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Doc_Definitions(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Modifications_Tactics(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Metadata.c.trace b/server/nng/build/ir/NNG/Metadata.c.trace
new file mode 100644
index 0000000..0a81af6
--- /dev/null
+++ b/server/nng/build/ir/NNG/Metadata.c.trace
@@ -0,0 +1 @@
+10126315224814379241
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/Modifications/Tactics.c b/server/nng/build/ir/NNG/Modifications/Tactics.c
new file mode 100644
index 0000000..23f8c1d
--- /dev/null
+++ b/server/nng/build/ir/NNG/Modifications/Tactics.c
@@ -0,0 +1,3061 @@
+// Lean compiler output
+// Module: NNG.Modifications.Tactics
+// Imports: Init Mathlib.Lean.Expr.Basic NNG.MyNat.Addition Lean.Elab.Tactic.Basic
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* l_Lean_Meta_getElimInfo(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Meta_FVarSubst_apply(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_induction;
+lean_object* l___private_Init_Util_0__outOfBounds___rarg(lean_object*);
+static lean_object* l_MyNat_induction___closed__14;
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__7;
+lean_object* l_Lean_Elab_Tactic_withRWRulesSeq(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Meta_throwTacticEx___rarg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* lean_mk_empty_array_with_capacity(lean_object*);
+lean_object* l___private_Lean_Expr_0__Lean_Expr_getAppNumArgsAux(lean_object*, lean_object*);
+static lean_object* l_MyNat_rfl___closed__4;
+extern lean_object* l_Lean_Parser_Tactic_location;
+static lean_object* l_MyNat_induction___closed__7;
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic_ElimApp_evalNames(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_expandOptLocation(lean_object*);
+lean_object* l_Lean_Meta_mkGeneralizationForbiddenSet(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_evalRfl___rarg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Expr_sort___override(lean_object*);
+lean_object* lean_array_push(lean_object*, lean_object*);
+lean_object* l_Lean_MVarId_assign___at_Lean_Elab_Tactic_closeMainGoal___spec__1(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* lean_mk_array(lean_object*, lean_object*);
+uint8_t lean_usize_dec_eq(size_t, size_t);
+static lean_object* l_MyNat_induction___closed__11;
+lean_object* l_Lean_Syntax_getArgs(lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__10;
+lean_object* l_Lean_replaceRef(lean_object*, lean_object*);
+extern lean_object* l_Lean_Parser_Tactic_casesTarget;
+lean_object* lean_array_fget(lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_getMainGoal(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_MVarId_getTag(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_Array_foldlMUnsafe_fold___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__3___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__24;
+lean_object* l_Lean_MVarId_refl(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+uint8_t l_Lean_Syntax_isOfKind(lean_object*, lean_object*);
+static lean_object* l_Lean_Parser_Tactic_ElimApp_evalNames___closed__1;
+LEAN_EXPORT lean_object* l_MyNat_evalRfl(lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__7;
+static lean_object* l_MyNat_rewriteSeq___closed__5;
+static lean_object* l_MyNat_induction___closed__12;
+lean_object* l_Lean_Elab_Tactic_throwNoGoalsToBeSolved___rarg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_throwUnsupportedSyntax___at_Std_Tactic___aux__Std__Tactic__ShowTerm______elabRules__Std__Tactic__showTermTac__1___spec__1___rarg(lean_object*);
+lean_object* l_Lean_MVarId_withContext___at_Lean_Elab_Term_logUnassignedUsingErrorInfos___spec__4___rarg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__12;
+static lean_object* l_MyNat_evalRewriteSeq___lambda__2___closed__1;
+lean_object* l_Lean_Elab_Tactic_ElimApp_mkElimApp(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_List_appendTR___rarg(lean_object*, lean_object*);
+size_t lean_usize_of_nat(lean_object*);
+lean_object* l_Lean_Elab_Tactic_getNameOfIdent_x27(lean_object*);
+lean_object* l_Lean_Elab_Tactic_getUnsolvedGoals(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__15;
+static lean_object* l_MyNat_induction___closed__17;
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___boxed(lean_object**);
+static lean_object* l_MyNat_rewriteSeq___closed__11;
+lean_object* l_Lean_Elab_Tactic_withLocation(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_rewriteLocalDecl(lean_object*, uint8_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_SourceInfo_fromRef(lean_object*, uint8_t);
+static lean_object* l_MyNat_rewriteSeq___closed__1;
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__4;
+static lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___closed__1;
+static lean_object* l_MyNat_induction___closed__8;
+static lean_object* l_MyNat_evalRewriteSeq___lambda__2___closed__4;
+extern lean_object* l_Lean_Parser_Tactic_rwRuleSeq;
+lean_object* l_Lean_Elab_Tactic_elabCasesTargets(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_withMainContext___rarg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__6;
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__2___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* lean_array_to_list(lean_object*, lean_object*);
+lean_object* l_Lean_MVarId_withContext___at_Lean_Elab_Tactic_withMainContext___spec__1___rarg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__20;
+static lean_object* l_MyNat_induction___closed__9;
+LEAN_EXPORT lean_object* l_MyNat_evalRfl___boxed(lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__3(lean_object*, lean_object*, uint8_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+extern lean_object* l_Lean_levelZero;
+lean_object* l_Lean_MVarId_revert(lean_object*, lean_object*, uint8_t, uint8_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+extern lean_object* l_Lean_instInhabitedExpr;
+lean_object* l_Lean_Meta_addImplicitTargets(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_rfl___closed__2;
+static lean_object* l_MyNat_induction___closed__15;
+static lean_object* l_MyNat_rewriteSeq___closed__6;
+lean_object* l_Lean_Expr_addLocalVarInfoForBinderIdent(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Syntax_getSepArgs(lean_object*);
+static lean_object* l_MyNat_induction___closed__16;
+lean_object* l_Lean_Name_str___override(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__1(lean_object*, uint8_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__22;
+lean_object* l_Lean_Syntax_getArg(lean_object*, lean_object*);
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1;
+static lean_object* l_MyNat_rfl___closed__1;
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__2(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__3;
+static lean_object* l_MyNat_evalRfl___rarg___closed__1;
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2;
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__1___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__5;
+lean_object* l_Array_append___rarg(lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_rewriteTarget___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__14;
+static lean_object* l_MyNat_induction___closed__10;
+static lean_object* l_MyNat_rewriteSeq___closed__9;
+lean_object* l_Lean_Name_mkStr6(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__1;
+static lean_object* l_MyNat_rewriteSeq___closed__2;
+lean_object* l_Lean_Meta_introNCore(lean_object*, lean_object*, lean_object*, uint8_t, uint8_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__8;
+static lean_object* l_MyNat_evalRewriteSeq___lambda__2___closed__5;
+static lean_object* l_MyNat_induction___closed__5;
+static lean_object* l_MyNat_rewriteSeq___closed__4;
+static lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__2;
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__3___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+uint8_t lean_nat_dec_lt(lean_object*, lean_object*);
+static lean_object* l_MyNat_evalRewriteSeq___lambda__3___closed__1;
+lean_object* l_Lean_Name_mkStr2(lean_object*, lean_object*);
+static lean_object* l_MyNat_rfl___closed__3;
+static lean_object* l_MyNat_induction___closed__21;
+lean_object* l_Lean_Meta_getFVarSetToGeneralize(lean_object*, lean_object*, uint8_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Syntax_node1(lean_object*, lean_object*, lean_object*);
+extern lean_object* l_Lean_binderIdent;
+lean_object* l_Lean_RBTree_toArray___at_Lean_Meta_getFVarsToGeneralize___spec__1(lean_object*);
+static lean_object* l_MyNat_induction___closed__4;
+static lean_object* l_MyNat_induction___closed__2;
+lean_object* lean_nat_sub(lean_object*, lean_object*);
+lean_object* l_Lean_MVarId_tryClear(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__23;
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic_ElimApp_evalNames___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_elabRewriteConfig(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_List_splitAtD___rarg(lean_object*, lean_object*, lean_object*);
+lean_object* l_List_reverse___rarg(lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__3;
+LEAN_EXPORT lean_object* l_MyNat_rfl;
+size_t lean_usize_add(size_t, size_t);
+static lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__1;
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__2___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__13;
+LEAN_EXPORT lean_object* l_Array_foldlMUnsafe_fold___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__3(lean_object*, size_t, size_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* lean_array_uget(lean_object*, size_t);
+lean_object* l_Lean_Expr_fvar___override(lean_object*);
+static lean_object* l_MyNat_induction___closed__19;
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_rewriteSeq___closed__8;
+extern lean_object* l_Lean_Parser_Tactic_config;
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__9;
+lean_object* l___private_Lean_Elab_Tactic_Induction_0__Lean_Elab_Tactic_ElimApp_getAltNumFields(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_evalRfl___rarg___lambda__1(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Name_mkStr4(lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l___private_Lean_Expr_0__Lean_Expr_getAppArgsAux(lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Meta_sortFVarIds(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3;
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, size_t, size_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_evalInduction_checkTargets(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* lean_array_get_size(lean_object*);
+lean_object* l_Array_mapMUnsafe_map___at_Lean_Elab_Tactic_evalInduction___spec__2(size_t, size_t, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_rewriteSeq;
+uint8_t lean_nat_dec_le(lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__6;
+uint8_t lean_usize_dec_lt(size_t, size_t);
+lean_object* l_Lean_Meta_Cases_unifyEqs_x3f(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_setGoals(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__2(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__2(lean_object*, lean_object*, lean_object*, size_t, size_t, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__18;
+LEAN_EXPORT lean_object* l_List_mapTR_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__1(lean_object*, lean_object*);
+lean_object* l_Lean_Expr_mvarId_x21(lean_object*);
+static lean_object* l_MyNat_evalRewriteSeq___lambda__2___closed__3;
+lean_object* l_Lean_Elab_Tactic_replaceMainGoal(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Elab_Tactic_ElimApp_setMotiveArg(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_evalRewriteSeq___lambda__2___closed__2;
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___boxed(lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*, lean_object*);
+static lean_object* l_MyNat_induction___closed__13;
+static lean_object* _init_l_MyNat_rewriteSeq___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("MyNat", 5);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__2() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("rewriteSeq", 10);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__3() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__1;
+x_2 = l_MyNat_rewriteSeq___closed__2;
+x_3 = l_Lean_Name_mkStr2(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__4() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("andthen", 7);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__5() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l_MyNat_rewriteSeq___closed__4;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__6() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("rw", 2);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__7() {
+_start:
+{
+lean_object* x_1; uint8_t x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__6;
+x_2 = 0;
+x_3 = lean_alloc_ctor(6, 1, 1);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set_uint8(x_3, sizeof(void*)*1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__8() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("optional", 8);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__9() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l_MyNat_rewriteSeq___closed__8;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__10() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__9;
+x_2 = l_Lean_Parser_Tactic_config;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set(x_3, 1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__11() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_rewriteSeq___closed__7;
+x_3 = l_MyNat_rewriteSeq___closed__10;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__12() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_rewriteSeq___closed__11;
+x_3 = l_Lean_Parser_Tactic_rwRuleSeq;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__13() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__9;
+x_2 = l_Lean_Parser_Tactic_location;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set(x_3, 1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__14() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_rewriteSeq___closed__12;
+x_3 = l_MyNat_rewriteSeq___closed__13;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq___closed__15() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__3;
+x_2 = lean_unsigned_to_nat(1022u);
+x_3 = l_MyNat_rewriteSeq___closed__14;
+x_4 = lean_alloc_ctor(3, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_rewriteSeq() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_MyNat_rewriteSeq___closed__15;
+return x_1;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__1(lean_object* x_1, uint8_t x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+lean_object* x_14; 
+x_14 = l_Lean_Elab_Tactic_rewriteLocalDecl(x_1, x_2, x_4, x_3, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+return x_14;
+}
+}
+static lean_object* _init_l_MyNat_evalRewriteSeq___lambda__2___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("rewrite", 7);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_evalRewriteSeq___lambda__2___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l_MyNat_evalRewriteSeq___lambda__2___closed__1;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_evalRewriteSeq___lambda__2___closed__3() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("did not find instance of the pattern in the current goal", 56);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_evalRewriteSeq___lambda__2___closed__4() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_MyNat_evalRewriteSeq___lambda__2___closed__3;
+x_2 = lean_alloc_ctor(3, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_evalRewriteSeq___lambda__2___closed__5() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_MyNat_evalRewriteSeq___lambda__2___closed__4;
+x_2 = lean_alloc_ctor(0, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__2(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10) {
+_start:
+{
+lean_object* x_11; lean_object* x_12; lean_object* x_13; 
+x_11 = l_MyNat_evalRewriteSeq___lambda__2___closed__2;
+x_12 = l_MyNat_evalRewriteSeq___lambda__2___closed__5;
+x_13 = l_Lean_Meta_throwTacticEx___rarg(x_11, x_1, x_12, x_6, x_7, x_8, x_9, x_10);
+return x_13;
+}
+}
+static lean_object* _init_l_MyNat_evalRewriteSeq___lambda__3___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_alloc_closure((void*)(l_MyNat_evalRewriteSeq___lambda__2___boxed), 10, 0);
+return x_1;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__3(lean_object* x_1, lean_object* x_2, uint8_t x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+lean_object* x_14; lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; lean_object* x_19; 
+x_14 = lean_box(x_3);
+lean_inc(x_1);
+lean_inc(x_4);
+x_15 = lean_alloc_closure((void*)(l_MyNat_evalRewriteSeq___lambda__1___boxed), 13, 3);
+lean_closure_set(x_15, 0, x_4);
+lean_closure_set(x_15, 1, x_14);
+lean_closure_set(x_15, 2, x_1);
+x_16 = lean_box(x_3);
+x_17 = lean_alloc_closure((void*)(l_Lean_Elab_Tactic_rewriteTarget___boxed), 12, 3);
+lean_closure_set(x_17, 0, x_4);
+lean_closure_set(x_17, 1, x_16);
+lean_closure_set(x_17, 2, x_1);
+x_18 = l_MyNat_evalRewriteSeq___lambda__3___closed__1;
+x_19 = l_Lean_Elab_Tactic_withLocation(x_2, x_15, x_17, x_18, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+return x_19;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10) {
+_start:
+{
+lean_object* x_11; lean_object* x_12; lean_object* x_13; 
+x_11 = lean_unsigned_to_nat(1u);
+x_12 = l_Lean_Syntax_getArg(x_1, x_11);
+lean_inc(x_9);
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_6);
+lean_inc(x_5);
+lean_inc(x_4);
+x_13 = l_Lean_Elab_Tactic_elabRewriteConfig(x_12, x_4, x_5, x_6, x_7, x_8, x_9, x_10);
+lean_dec(x_12);
+if (lean_obj_tag(x_13) == 0)
+{
+lean_object* x_14; lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; lean_object* x_19; lean_object* x_20; lean_object* x_21; lean_object* x_22; lean_object* x_23; lean_object* x_24; 
+x_14 = lean_ctor_get(x_13, 0);
+lean_inc(x_14);
+x_15 = lean_ctor_get(x_13, 1);
+lean_inc(x_15);
+lean_dec(x_13);
+x_16 = lean_unsigned_to_nat(3u);
+x_17 = l_Lean_Syntax_getArg(x_1, x_16);
+x_18 = l_Lean_Elab_Tactic_expandOptLocation(x_17);
+lean_dec(x_17);
+x_19 = lean_unsigned_to_nat(0u);
+x_20 = l_Lean_Syntax_getArg(x_1, x_19);
+x_21 = lean_unsigned_to_nat(2u);
+x_22 = l_Lean_Syntax_getArg(x_1, x_21);
+x_23 = lean_alloc_closure((void*)(l_MyNat_evalRewriteSeq___lambda__3___boxed), 13, 2);
+lean_closure_set(x_23, 0, x_14);
+lean_closure_set(x_23, 1, x_18);
+x_24 = l_Lean_Elab_Tactic_withRWRulesSeq(x_20, x_22, x_23, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_15);
+lean_dec(x_22);
+return x_24;
+}
+else
+{
+uint8_t x_25; 
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+x_25 = !lean_is_exclusive(x_13);
+if (x_25 == 0)
+{
+return x_13;
+}
+else
+{
+lean_object* x_26; lean_object* x_27; lean_object* x_28; 
+x_26 = lean_ctor_get(x_13, 0);
+x_27 = lean_ctor_get(x_13, 1);
+lean_inc(x_27);
+lean_inc(x_26);
+lean_dec(x_13);
+x_28 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_28, 0, x_26);
+lean_ctor_set(x_28, 1, x_27);
+return x_28;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__1___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+uint8_t x_14; lean_object* x_15; 
+x_14 = lean_unbox(x_2);
+lean_dec(x_2);
+x_15 = l_MyNat_evalRewriteSeq___lambda__1(x_1, x_14, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+return x_15;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__2___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10) {
+_start:
+{
+lean_object* x_11; 
+x_11 = l_MyNat_evalRewriteSeq___lambda__2(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10);
+lean_dec(x_9);
+lean_dec(x_7);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+return x_11;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___lambda__3___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+uint8_t x_14; lean_object* x_15; 
+x_14 = lean_unbox(x_3);
+lean_dec(x_3);
+x_15 = l_MyNat_evalRewriteSeq___lambda__3(x_1, x_2, x_14, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+lean_dec(x_2);
+return x_15;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRewriteSeq___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10) {
+_start:
+{
+lean_object* x_11; 
+x_11 = l_MyNat_evalRewriteSeq(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10);
+lean_dec(x_1);
+return x_11;
+}
+}
+LEAN_EXPORT lean_object* l_List_mapTR_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__1(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+if (lean_obj_tag(x_1) == 0)
+{
+lean_object* x_3; 
+x_3 = l_List_reverse___rarg(x_2);
+return x_3;
+}
+else
+{
+uint8_t x_4; 
+x_4 = !lean_is_exclusive(x_1);
+if (x_4 == 0)
+{
+lean_object* x_5; lean_object* x_6; lean_object* x_7; lean_object* x_8; lean_object* x_9; 
+x_5 = lean_ctor_get(x_1, 0);
+x_6 = lean_ctor_get(x_1, 1);
+x_7 = lean_unsigned_to_nat(0u);
+x_8 = l_Lean_Syntax_getArg(x_5, x_7);
+lean_dec(x_5);
+x_9 = l_Lean_Elab_Tactic_getNameOfIdent_x27(x_8);
+lean_dec(x_8);
+lean_ctor_set(x_1, 1, x_2);
+lean_ctor_set(x_1, 0, x_9);
+{
+lean_object* _tmp_0 = x_6;
+lean_object* _tmp_1 = x_1;
+x_1 = _tmp_0;
+x_2 = _tmp_1;
+}
+goto _start;
+}
+else
+{
+lean_object* x_11; lean_object* x_12; lean_object* x_13; lean_object* x_14; lean_object* x_15; lean_object* x_16; 
+x_11 = lean_ctor_get(x_1, 0);
+x_12 = lean_ctor_get(x_1, 1);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_dec(x_1);
+x_13 = lean_unsigned_to_nat(0u);
+x_14 = l_Lean_Syntax_getArg(x_11, x_13);
+lean_dec(x_11);
+x_15 = l_Lean_Elab_Tactic_getNameOfIdent_x27(x_14);
+lean_dec(x_14);
+x_16 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_16, 0, x_15);
+lean_ctor_set(x_16, 1, x_2);
+x_1 = x_12;
+x_2 = x_16;
+goto _start;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__2(lean_object* x_1, lean_object* x_2, lean_object* x_3, size_t x_4, size_t x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+uint8_t x_14; 
+x_14 = lean_usize_dec_lt(x_5, x_4);
+if (x_14 == 0)
+{
+lean_object* x_15; 
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_2);
+x_15 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_15, 0, x_6);
+lean_ctor_set(x_15, 1, x_13);
+return x_15;
+}
+else
+{
+lean_object* x_16; 
+x_16 = lean_array_uget(x_3, x_5);
+if (lean_obj_tag(x_6) == 0)
+{
+lean_object* x_17; 
+lean_dec(x_16);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_2);
+x_17 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_17, 0, x_6);
+lean_ctor_set(x_17, 1, x_13);
+return x_17;
+}
+else
+{
+lean_object* x_18; lean_object* x_19; lean_object* x_20; lean_object* x_21; lean_object* x_22; lean_object* x_23; 
+x_18 = lean_ctor_get(x_6, 0);
+lean_inc(x_18);
+x_19 = lean_ctor_get(x_6, 1);
+lean_inc(x_19);
+lean_dec(x_6);
+x_20 = l_Lean_Expr_fvar___override(x_16);
+x_21 = l_Lean_Meta_FVarSubst_apply(x_1, x_20);
+x_22 = lean_alloc_closure((void*)(l_Lean_Expr_addLocalVarInfoForBinderIdent), 9, 2);
+lean_closure_set(x_22, 0, x_21);
+lean_closure_set(x_22, 1, x_18);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_inc(x_10);
+lean_inc(x_9);
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_2);
+x_23 = l_Lean_MVarId_withContext___at_Lean_Elab_Term_logUnassignedUsingErrorInfos___spec__4___rarg(x_2, x_22, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+if (lean_obj_tag(x_23) == 0)
+{
+lean_object* x_24; size_t x_25; size_t x_26; 
+x_24 = lean_ctor_get(x_23, 1);
+lean_inc(x_24);
+lean_dec(x_23);
+x_25 = 1;
+x_26 = lean_usize_add(x_5, x_25);
+x_5 = x_26;
+x_6 = x_19;
+x_13 = x_24;
+goto _start;
+}
+else
+{
+uint8_t x_28; 
+lean_dec(x_19);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_2);
+x_28 = !lean_is_exclusive(x_23);
+if (x_28 == 0)
+{
+return x_23;
+}
+else
+{
+lean_object* x_29; lean_object* x_30; lean_object* x_31; 
+x_29 = lean_ctor_get(x_23, 0);
+x_30 = lean_ctor_get(x_23, 1);
+lean_inc(x_30);
+lean_inc(x_29);
+lean_dec(x_23);
+x_31 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_31, 0, x_29);
+lean_ctor_set(x_31, 1, x_30);
+return x_31;
+}
+}
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_Array_foldlMUnsafe_fold___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__3(lean_object* x_1, size_t x_2, size_t x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9) {
+_start:
+{
+uint8_t x_10; 
+x_10 = lean_usize_dec_eq(x_2, x_3);
+if (x_10 == 0)
+{
+lean_object* x_11; lean_object* x_12; 
+x_11 = lean_array_uget(x_1, x_2);
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_6);
+lean_inc(x_5);
+x_12 = l_Lean_MVarId_tryClear(x_4, x_11, x_5, x_6, x_7, x_8, x_9);
+if (lean_obj_tag(x_12) == 0)
+{
+lean_object* x_13; lean_object* x_14; size_t x_15; size_t x_16; 
+x_13 = lean_ctor_get(x_12, 0);
+lean_inc(x_13);
+x_14 = lean_ctor_get(x_12, 1);
+lean_inc(x_14);
+lean_dec(x_12);
+x_15 = 1;
+x_16 = lean_usize_add(x_2, x_15);
+x_2 = x_16;
+x_4 = x_13;
+x_9 = x_14;
+goto _start;
+}
+else
+{
+uint8_t x_18; 
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+x_18 = !lean_is_exclusive(x_12);
+if (x_18 == 0)
+{
+return x_12;
+}
+else
+{
+lean_object* x_19; lean_object* x_20; lean_object* x_21; 
+x_19 = lean_ctor_get(x_12, 0);
+x_20 = lean_ctor_get(x_12, 1);
+lean_inc(x_20);
+lean_inc(x_19);
+lean_dec(x_12);
+x_21 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_21, 0, x_19);
+lean_ctor_set(x_21, 1, x_20);
+return x_21;
+}
+}
+}
+else
+{
+lean_object* x_22; 
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+x_22 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_22, 0, x_4);
+lean_ctor_set(x_22, 1, x_9);
+return x_22;
+}
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1() {
+_start:
+{
+lean_object* x_1; uint8_t x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = 0;
+x_3 = l_Lean_SourceInfo_fromRef(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Lean", 4);
+return x_1;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Parser", 6);
+return x_1;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__4() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Term", 4);
+return x_1;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__5() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("hole", 4);
+return x_1;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__6() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; lean_object* x_5; 
+x_1 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2;
+x_2 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3;
+x_3 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__4;
+x_4 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__5;
+x_5 = l_Lean_Name_mkStr4(x_1, x_2, x_3, x_4);
+return x_5;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__7() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("_", 1);
+return x_1;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__8() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1;
+x_2 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__7;
+x_3 = lean_alloc_ctor(2, 2, 0);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set(x_3, 1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__9() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1;
+x_2 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__6;
+x_3 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__8;
+x_4 = l_Lean_Syntax_node1(x_1, x_2, x_3);
+return x_4;
+}
+}
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, size_t x_6, size_t x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13, lean_object* x_14, lean_object* x_15) {
+_start:
+{
+uint8_t x_16; 
+x_16 = lean_usize_dec_lt(x_7, x_6);
+if (x_16 == 0)
+{
+lean_object* x_17; 
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_17 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_17, 0, x_8);
+lean_ctor_set(x_17, 1, x_15);
+return x_17;
+}
+else
+{
+lean_object* x_18; lean_object* x_19; lean_object* x_20; lean_object* x_26; lean_object* x_27; lean_object* x_28; lean_object* x_29; lean_object* x_30; lean_object* x_31; 
+x_18 = lean_array_uget(x_5, x_7);
+x_26 = lean_ctor_get(x_18, 0);
+lean_inc(x_26);
+x_27 = lean_ctor_get(x_18, 2);
+lean_inc(x_27);
+lean_dec(x_18);
+x_28 = lean_ctor_get(x_8, 0);
+lean_inc(x_28);
+x_29 = lean_ctor_get(x_8, 1);
+lean_inc(x_29);
+if (lean_is_exclusive(x_8)) {
+ lean_ctor_release(x_8, 0);
+ lean_ctor_release(x_8, 1);
+ x_30 = x_8;
+} else {
+ lean_dec_ref(x_8);
+ x_30 = lean_box(0);
+}
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_inc(x_10);
+lean_inc(x_9);
+lean_inc(x_1);
+x_31 = l___private_Lean_Elab_Tactic_Induction_0__Lean_Elab_Tactic_ElimApp_getAltNumFields(x_1, x_26, x_9, x_10, x_11, x_12, x_13, x_14, x_15);
+if (lean_obj_tag(x_31) == 0)
+{
+lean_object* x_32; lean_object* x_33; lean_object* x_34; lean_object* x_35; lean_object* x_36; lean_object* x_37; lean_object* x_38; lean_object* x_39; uint8_t x_40; lean_object* x_41; 
+x_32 = lean_ctor_get(x_31, 0);
+lean_inc(x_32);
+x_33 = lean_ctor_get(x_31, 1);
+lean_inc(x_33);
+lean_dec(x_31);
+x_34 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__9;
+lean_inc(x_32);
+x_35 = l_List_splitAtD___rarg(x_32, x_28, x_34);
+x_36 = lean_ctor_get(x_35, 0);
+lean_inc(x_36);
+x_37 = lean_ctor_get(x_35, 1);
+lean_inc(x_37);
+lean_dec(x_35);
+x_38 = lean_box(0);
+lean_inc(x_36);
+x_39 = l_List_mapTR_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__1(x_36, x_38);
+x_40 = 0;
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+x_41 = l_Lean_Meta_introNCore(x_27, x_32, x_39, x_40, x_40, x_11, x_12, x_13, x_14, x_33);
+if (lean_obj_tag(x_41) == 0)
+{
+lean_object* x_42; lean_object* x_43; lean_object* x_44; lean_object* x_45; lean_object* x_46; lean_object* x_47; lean_object* x_48; 
+x_42 = lean_ctor_get(x_41, 0);
+lean_inc(x_42);
+x_43 = lean_ctor_get(x_41, 1);
+lean_inc(x_43);
+lean_dec(x_41);
+x_44 = lean_ctor_get(x_42, 0);
+lean_inc(x_44);
+x_45 = lean_ctor_get(x_42, 1);
+lean_inc(x_45);
+lean_dec(x_42);
+x_46 = lean_box(0);
+x_47 = lean_box(0);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_inc(x_2);
+x_48 = l_Lean_Meta_Cases_unifyEqs_x3f(x_2, x_45, x_46, x_47, x_11, x_12, x_13, x_14, x_43);
+if (lean_obj_tag(x_48) == 0)
+{
+lean_object* x_49; 
+x_49 = lean_ctor_get(x_48, 0);
+lean_inc(x_49);
+if (lean_obj_tag(x_49) == 0)
+{
+lean_object* x_50; lean_object* x_51; lean_object* x_52; 
+lean_dec(x_44);
+lean_dec(x_36);
+x_50 = lean_ctor_get(x_48, 1);
+lean_inc(x_50);
+lean_dec(x_48);
+if (lean_is_scalar(x_30)) {
+ x_51 = lean_alloc_ctor(0, 2, 0);
+} else {
+ x_51 = x_30;
+}
+lean_ctor_set(x_51, 0, x_37);
+lean_ctor_set(x_51, 1, x_29);
+x_52 = lean_alloc_ctor(1, 1, 0);
+lean_ctor_set(x_52, 0, x_51);
+x_19 = x_52;
+x_20 = x_50;
+goto block_25;
+}
+else
+{
+lean_object* x_53; lean_object* x_54; lean_object* x_55; lean_object* x_56; lean_object* x_57; lean_object* x_58; uint8_t x_72; lean_object* x_73; 
+x_53 = lean_ctor_get(x_49, 0);
+lean_inc(x_53);
+lean_dec(x_49);
+x_54 = lean_ctor_get(x_48, 1);
+lean_inc(x_54);
+lean_dec(x_48);
+x_55 = lean_ctor_get(x_53, 0);
+lean_inc(x_55);
+x_56 = lean_ctor_get(x_53, 1);
+lean_inc(x_56);
+lean_dec(x_53);
+x_72 = 1;
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_inc(x_3);
+x_73 = l_Lean_Meta_introNCore(x_55, x_3, x_38, x_40, x_72, x_11, x_12, x_13, x_14, x_54);
+if (lean_obj_tag(x_73) == 0)
+{
+lean_object* x_74; lean_object* x_75; lean_object* x_76; lean_object* x_77; lean_object* x_78; uint8_t x_79; 
+x_74 = lean_ctor_get(x_73, 0);
+lean_inc(x_74);
+x_75 = lean_ctor_get(x_73, 1);
+lean_inc(x_75);
+lean_dec(x_73);
+x_76 = lean_ctor_get(x_74, 1);
+lean_inc(x_76);
+lean_dec(x_74);
+x_77 = lean_array_get_size(x_4);
+x_78 = lean_unsigned_to_nat(0u);
+x_79 = lean_nat_dec_lt(x_78, x_77);
+if (x_79 == 0)
+{
+lean_dec(x_77);
+x_57 = x_76;
+x_58 = x_75;
+goto block_71;
+}
+else
+{
+uint8_t x_80; 
+x_80 = lean_nat_dec_le(x_77, x_77);
+if (x_80 == 0)
+{
+lean_dec(x_77);
+x_57 = x_76;
+x_58 = x_75;
+goto block_71;
+}
+else
+{
+size_t x_81; size_t x_82; lean_object* x_83; 
+x_81 = 0;
+x_82 = lean_usize_of_nat(x_77);
+lean_dec(x_77);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+x_83 = l_Array_foldlMUnsafe_fold___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__3(x_4, x_81, x_82, x_76, x_11, x_12, x_13, x_14, x_75);
+if (lean_obj_tag(x_83) == 0)
+{
+lean_object* x_84; lean_object* x_85; 
+x_84 = lean_ctor_get(x_83, 0);
+lean_inc(x_84);
+x_85 = lean_ctor_get(x_83, 1);
+lean_inc(x_85);
+lean_dec(x_83);
+x_57 = x_84;
+x_58 = x_85;
+goto block_71;
+}
+else
+{
+uint8_t x_86; 
+lean_dec(x_56);
+lean_dec(x_44);
+lean_dec(x_37);
+lean_dec(x_36);
+lean_dec(x_30);
+lean_dec(x_29);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_86 = !lean_is_exclusive(x_83);
+if (x_86 == 0)
+{
+return x_83;
+}
+else
+{
+lean_object* x_87; lean_object* x_88; lean_object* x_89; 
+x_87 = lean_ctor_get(x_83, 0);
+x_88 = lean_ctor_get(x_83, 1);
+lean_inc(x_88);
+lean_inc(x_87);
+lean_dec(x_83);
+x_89 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_89, 0, x_87);
+lean_ctor_set(x_89, 1, x_88);
+return x_89;
+}
+}
+}
+}
+}
+else
+{
+uint8_t x_90; 
+lean_dec(x_56);
+lean_dec(x_44);
+lean_dec(x_37);
+lean_dec(x_36);
+lean_dec(x_30);
+lean_dec(x_29);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_90 = !lean_is_exclusive(x_73);
+if (x_90 == 0)
+{
+return x_73;
+}
+else
+{
+lean_object* x_91; lean_object* x_92; lean_object* x_93; 
+x_91 = lean_ctor_get(x_73, 0);
+x_92 = lean_ctor_get(x_73, 1);
+lean_inc(x_92);
+lean_inc(x_91);
+lean_dec(x_73);
+x_93 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_93, 0, x_91);
+lean_ctor_set(x_93, 1, x_92);
+return x_93;
+}
+}
+block_71:
+{
+lean_object* x_59; size_t x_60; size_t x_61; lean_object* x_62; 
+x_59 = lean_array_get_size(x_44);
+x_60 = lean_usize_of_nat(x_59);
+lean_dec(x_59);
+x_61 = 0;
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_inc(x_10);
+lean_inc(x_9);
+lean_inc(x_57);
+x_62 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__2(x_56, x_57, x_44, x_60, x_61, x_36, x_9, x_10, x_11, x_12, x_13, x_14, x_58);
+lean_dec(x_44);
+lean_dec(x_56);
+if (lean_obj_tag(x_62) == 0)
+{
+lean_object* x_63; lean_object* x_64; lean_object* x_65; lean_object* x_66; 
+x_63 = lean_ctor_get(x_62, 1);
+lean_inc(x_63);
+lean_dec(x_62);
+x_64 = lean_array_push(x_29, x_57);
+if (lean_is_scalar(x_30)) {
+ x_65 = lean_alloc_ctor(0, 2, 0);
+} else {
+ x_65 = x_30;
+}
+lean_ctor_set(x_65, 0, x_37);
+lean_ctor_set(x_65, 1, x_64);
+x_66 = lean_alloc_ctor(1, 1, 0);
+lean_ctor_set(x_66, 0, x_65);
+x_19 = x_66;
+x_20 = x_63;
+goto block_25;
+}
+else
+{
+uint8_t x_67; 
+lean_dec(x_57);
+lean_dec(x_37);
+lean_dec(x_30);
+lean_dec(x_29);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_67 = !lean_is_exclusive(x_62);
+if (x_67 == 0)
+{
+return x_62;
+}
+else
+{
+lean_object* x_68; lean_object* x_69; lean_object* x_70; 
+x_68 = lean_ctor_get(x_62, 0);
+x_69 = lean_ctor_get(x_62, 1);
+lean_inc(x_69);
+lean_inc(x_68);
+lean_dec(x_62);
+x_70 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_70, 0, x_68);
+lean_ctor_set(x_70, 1, x_69);
+return x_70;
+}
+}
+}
+}
+}
+else
+{
+uint8_t x_94; 
+lean_dec(x_44);
+lean_dec(x_37);
+lean_dec(x_36);
+lean_dec(x_30);
+lean_dec(x_29);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_94 = !lean_is_exclusive(x_48);
+if (x_94 == 0)
+{
+return x_48;
+}
+else
+{
+lean_object* x_95; lean_object* x_96; lean_object* x_97; 
+x_95 = lean_ctor_get(x_48, 0);
+x_96 = lean_ctor_get(x_48, 1);
+lean_inc(x_96);
+lean_inc(x_95);
+lean_dec(x_48);
+x_97 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_97, 0, x_95);
+lean_ctor_set(x_97, 1, x_96);
+return x_97;
+}
+}
+}
+else
+{
+uint8_t x_98; 
+lean_dec(x_37);
+lean_dec(x_36);
+lean_dec(x_30);
+lean_dec(x_29);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_98 = !lean_is_exclusive(x_41);
+if (x_98 == 0)
+{
+return x_41;
+}
+else
+{
+lean_object* x_99; lean_object* x_100; lean_object* x_101; 
+x_99 = lean_ctor_get(x_41, 0);
+x_100 = lean_ctor_get(x_41, 1);
+lean_inc(x_100);
+lean_inc(x_99);
+lean_dec(x_41);
+x_101 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_101, 0, x_99);
+lean_ctor_set(x_101, 1, x_100);
+return x_101;
+}
+}
+}
+else
+{
+uint8_t x_102; 
+lean_dec(x_30);
+lean_dec(x_29);
+lean_dec(x_28);
+lean_dec(x_27);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_102 = !lean_is_exclusive(x_31);
+if (x_102 == 0)
+{
+return x_31;
+}
+else
+{
+lean_object* x_103; lean_object* x_104; lean_object* x_105; 
+x_103 = lean_ctor_get(x_31, 0);
+x_104 = lean_ctor_get(x_31, 1);
+lean_inc(x_104);
+lean_inc(x_103);
+lean_dec(x_31);
+x_105 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_105, 0, x_103);
+lean_ctor_set(x_105, 1, x_104);
+return x_105;
+}
+}
+block_25:
+{
+lean_object* x_21; size_t x_22; size_t x_23; 
+x_21 = lean_ctor_get(x_19, 0);
+lean_inc(x_21);
+lean_dec(x_19);
+x_22 = 1;
+x_23 = lean_usize_add(x_7, x_22);
+x_7 = x_23;
+x_8 = x_21;
+x_15 = x_20;
+goto _start;
+}
+}
+}
+}
+static lean_object* _init_l_Lean_Parser_Tactic_ElimApp_evalNames___closed__1() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = lean_unsigned_to_nat(0u);
+x_2 = lean_mk_empty_array_with_capacity(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic_ElimApp_evalNames(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+lean_object* x_14; lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; lean_object* x_19; lean_object* x_20; size_t x_21; size_t x_22; lean_object* x_23; 
+x_14 = lean_unsigned_to_nat(1u);
+x_15 = l_Lean_Syntax_getArg(x_3, x_14);
+x_16 = l_Lean_Syntax_getArgs(x_15);
+lean_dec(x_15);
+x_17 = lean_array_to_list(lean_box(0), x_16);
+x_18 = l_Lean_Parser_Tactic_ElimApp_evalNames___closed__1;
+x_19 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_19, 0, x_17);
+lean_ctor_set(x_19, 1, x_18);
+x_20 = lean_array_get_size(x_2);
+x_21 = lean_usize_of_nat(x_20);
+lean_dec(x_20);
+x_22 = 0;
+x_23 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4(x_1, x_4, x_5, x_6, x_2, x_21, x_22, x_19, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+if (lean_obj_tag(x_23) == 0)
+{
+uint8_t x_24; 
+x_24 = !lean_is_exclusive(x_23);
+if (x_24 == 0)
+{
+lean_object* x_25; lean_object* x_26; 
+x_25 = lean_ctor_get(x_23, 0);
+x_26 = lean_ctor_get(x_25, 1);
+lean_inc(x_26);
+lean_dec(x_25);
+lean_ctor_set(x_23, 0, x_26);
+return x_23;
+}
+else
+{
+lean_object* x_27; lean_object* x_28; lean_object* x_29; lean_object* x_30; 
+x_27 = lean_ctor_get(x_23, 0);
+x_28 = lean_ctor_get(x_23, 1);
+lean_inc(x_28);
+lean_inc(x_27);
+lean_dec(x_23);
+x_29 = lean_ctor_get(x_27, 1);
+lean_inc(x_29);
+lean_dec(x_27);
+x_30 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_30, 0, x_29);
+lean_ctor_set(x_30, 1, x_28);
+return x_30;
+}
+}
+else
+{
+uint8_t x_31; 
+x_31 = !lean_is_exclusive(x_23);
+if (x_31 == 0)
+{
+return x_23;
+}
+else
+{
+lean_object* x_32; lean_object* x_33; lean_object* x_34; 
+x_32 = lean_ctor_get(x_23, 0);
+x_33 = lean_ctor_get(x_23, 1);
+lean_inc(x_33);
+lean_inc(x_32);
+lean_dec(x_23);
+x_34 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_34, 0, x_32);
+lean_ctor_set(x_34, 1, x_33);
+return x_34;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__2___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+size_t x_14; size_t x_15; lean_object* x_16; 
+x_14 = lean_unbox_usize(x_4);
+lean_dec(x_4);
+x_15 = lean_unbox_usize(x_5);
+lean_dec(x_5);
+x_16 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__2(x_1, x_2, x_3, x_14, x_15, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+lean_dec(x_3);
+lean_dec(x_1);
+return x_16;
+}
+}
+LEAN_EXPORT lean_object* l_Array_foldlMUnsafe_fold___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__3___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9) {
+_start:
+{
+size_t x_10; size_t x_11; lean_object* x_12; 
+x_10 = lean_unbox_usize(x_2);
+lean_dec(x_2);
+x_11 = lean_unbox_usize(x_3);
+lean_dec(x_3);
+x_12 = l_Array_foldlMUnsafe_fold___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__3(x_1, x_10, x_11, x_4, x_5, x_6, x_7, x_8, x_9);
+lean_dec(x_1);
+return x_12;
+}
+}
+LEAN_EXPORT lean_object* l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13, lean_object* x_14, lean_object* x_15) {
+_start:
+{
+size_t x_16; size_t x_17; lean_object* x_18; 
+x_16 = lean_unbox_usize(x_6);
+lean_dec(x_6);
+x_17 = lean_unbox_usize(x_7);
+lean_dec(x_7);
+x_18 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4(x_1, x_2, x_3, x_4, x_5, x_16, x_17, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15);
+lean_dec(x_5);
+lean_dec(x_4);
+return x_18;
+}
+}
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic_ElimApp_evalNames___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13) {
+_start:
+{
+lean_object* x_14; 
+x_14 = l_Lean_Parser_Tactic_ElimApp_evalNames(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13);
+lean_dec(x_6);
+lean_dec(x_3);
+lean_dec(x_2);
+return x_14;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Tactic", 6);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__2() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("_root_", 6);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__3() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("induction", 9);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__4() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; lean_object* x_5; lean_object* x_6; lean_object* x_7; 
+x_1 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2;
+x_2 = l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3;
+x_3 = l_MyNat_induction___closed__1;
+x_4 = l_MyNat_induction___closed__2;
+x_5 = l_MyNat_rewriteSeq___closed__1;
+x_6 = l_MyNat_induction___closed__3;
+x_7 = l_Lean_Name_mkStr6(x_1, x_2, x_3, x_4, x_5, x_6);
+return x_7;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__5() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("induction ", 10);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__6() {
+_start:
+{
+lean_object* x_1; uint8_t x_2; lean_object* x_3; 
+x_1 = l_MyNat_induction___closed__5;
+x_2 = 0;
+x_3 = lean_alloc_ctor(6, 1, 1);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set_uint8(x_3, sizeof(void*)*1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__7() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes(", ", 2);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__8() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_MyNat_induction___closed__7;
+x_2 = lean_alloc_ctor(5, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__9() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes(",", 1);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__10() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; uint8_t x_4; lean_object* x_5; 
+x_1 = l_Lean_Parser_Tactic_casesTarget;
+x_2 = l_MyNat_induction___closed__9;
+x_3 = l_MyNat_induction___closed__8;
+x_4 = 0;
+x_5 = lean_alloc_ctor(11, 3, 1);
+lean_ctor_set(x_5, 0, x_1);
+lean_ctor_set(x_5, 1, x_2);
+lean_ctor_set(x_5, 2, x_3);
+lean_ctor_set_uint8(x_5, sizeof(void*)*3, x_4);
+return x_5;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__11() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_induction___closed__6;
+x_3 = l_MyNat_induction___closed__10;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__12() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes(" with ", 6);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__13() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_MyNat_induction___closed__12;
+x_2 = lean_alloc_ctor(5, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__14() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("many1", 5);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__15() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l_MyNat_induction___closed__14;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__16() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("colGt", 5);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__17() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l_MyNat_induction___closed__16;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__18() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_MyNat_induction___closed__17;
+x_2 = lean_alloc_ctor(0, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__19() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_induction___closed__18;
+x_3 = l_Lean_binderIdent;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__20() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_induction___closed__15;
+x_2 = l_MyNat_induction___closed__19;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set(x_3, 1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__21() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_induction___closed__13;
+x_3 = l_MyNat_induction___closed__20;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__22() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__9;
+x_2 = l_MyNat_induction___closed__21;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set(x_3, 1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__23() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rewriteSeq___closed__5;
+x_2 = l_MyNat_induction___closed__11;
+x_3 = l_MyNat_induction___closed__22;
+x_4 = lean_alloc_ctor(2, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_induction___closed__24() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_induction___closed__4;
+x_2 = lean_unsigned_to_nat(1022u);
+x_3 = l_MyNat_induction___closed__23;
+x_4 = lean_alloc_ctor(3, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_induction() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_MyNat_induction___closed__24;
+return x_1;
+}
+}
+static lean_object* _init_l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___closed__1() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_Lean_levelZero;
+x_2 = l_Lean_Expr_sort___override(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13, lean_object* x_14, lean_object* x_15, lean_object* x_16, lean_object* x_17) {
+_start:
+{
+lean_object* x_18; 
+lean_inc(x_16);
+lean_inc(x_15);
+lean_inc(x_14);
+lean_inc(x_13);
+x_18 = l_Lean_Meta_mkGeneralizationForbiddenSet(x_1, x_2, x_13, x_14, x_15, x_16, x_17);
+if (lean_obj_tag(x_18) == 0)
+{
+lean_object* x_19; lean_object* x_20; uint8_t x_21; lean_object* x_22; lean_object* x_23; lean_object* x_24; lean_object* x_25; lean_object* x_26; lean_object* x_27; lean_object* x_28; lean_object* x_29; 
+x_19 = lean_ctor_get(x_18, 0);
+lean_inc(x_19);
+x_20 = lean_ctor_get(x_18, 1);
+lean_inc(x_20);
+lean_dec(x_18);
+x_21 = 0;
+lean_inc(x_13);
+x_22 = l_Lean_Meta_getFVarSetToGeneralize(x_1, x_19, x_21, x_13, x_14, x_15, x_16, x_20);
+x_23 = lean_ctor_get(x_22, 0);
+lean_inc(x_23);
+x_24 = lean_ctor_get(x_22, 1);
+lean_inc(x_24);
+lean_dec(x_22);
+x_25 = l_Lean_RBTree_toArray___at_Lean_Meta_getFVarsToGeneralize___spec__1(x_23);
+lean_inc(x_13);
+x_26 = l_Lean_Meta_sortFVarIds(x_25, x_13, x_14, x_15, x_16, x_24);
+x_27 = lean_ctor_get(x_26, 0);
+lean_inc(x_27);
+x_28 = lean_ctor_get(x_26, 1);
+lean_inc(x_28);
+lean_dec(x_26);
+lean_inc(x_16);
+lean_inc(x_15);
+lean_inc(x_14);
+lean_inc(x_13);
+x_29 = l_Lean_MVarId_revert(x_3, x_27, x_21, x_21, x_13, x_14, x_15, x_16, x_28);
+if (lean_obj_tag(x_29) == 0)
+{
+lean_object* x_30; lean_object* x_31; lean_object* x_32; lean_object* x_33; lean_object* x_34; 
+x_30 = lean_ctor_get(x_29, 0);
+lean_inc(x_30);
+x_31 = lean_ctor_get(x_29, 1);
+lean_inc(x_31);
+lean_dec(x_29);
+x_32 = lean_ctor_get(x_30, 0);
+lean_inc(x_32);
+x_33 = lean_ctor_get(x_30, 1);
+lean_inc(x_33);
+lean_dec(x_30);
+lean_inc(x_33);
+x_34 = l_Lean_MVarId_getTag(x_33, x_13, x_14, x_15, x_16, x_31);
+if (lean_obj_tag(x_34) == 0)
+{
+lean_object* x_35; lean_object* x_36; lean_object* x_37; lean_object* x_38; lean_object* x_39; lean_object* x_40; lean_object* x_41; lean_object* x_42; lean_object* x_43; lean_object* x_44; lean_object* x_45; lean_object* x_46; lean_object* x_47; lean_object* x_48; lean_object* x_49; lean_object* x_50; 
+x_35 = lean_ctor_get(x_34, 0);
+lean_inc(x_35);
+x_36 = lean_ctor_get(x_34, 1);
+lean_inc(x_36);
+lean_dec(x_34);
+x_37 = lean_ctor_get(x_15, 0);
+lean_inc(x_37);
+x_38 = lean_ctor_get(x_15, 1);
+lean_inc(x_38);
+x_39 = lean_ctor_get(x_15, 2);
+lean_inc(x_39);
+x_40 = lean_ctor_get(x_15, 3);
+lean_inc(x_40);
+x_41 = lean_ctor_get(x_15, 4);
+lean_inc(x_41);
+x_42 = lean_ctor_get(x_15, 5);
+lean_inc(x_42);
+x_43 = lean_ctor_get(x_15, 6);
+lean_inc(x_43);
+x_44 = lean_ctor_get(x_15, 7);
+lean_inc(x_44);
+x_45 = lean_ctor_get(x_15, 8);
+lean_inc(x_45);
+x_46 = lean_ctor_get(x_15, 9);
+lean_inc(x_46);
+x_47 = lean_ctor_get(x_15, 10);
+lean_inc(x_47);
+x_48 = l_Lean_replaceRef(x_4, x_42);
+lean_dec(x_42);
+x_49 = lean_alloc_ctor(0, 11, 0);
+lean_ctor_set(x_49, 0, x_37);
+lean_ctor_set(x_49, 1, x_38);
+lean_ctor_set(x_49, 2, x_39);
+lean_ctor_set(x_49, 3, x_40);
+lean_ctor_set(x_49, 4, x_41);
+lean_ctor_set(x_49, 5, x_48);
+lean_ctor_set(x_49, 6, x_43);
+lean_ctor_set(x_49, 7, x_44);
+lean_ctor_set(x_49, 8, x_45);
+lean_ctor_set(x_49, 9, x_46);
+lean_ctor_set(x_49, 10, x_47);
+lean_inc(x_16);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+lean_inc(x_5);
+x_50 = l_Lean_Elab_Tactic_ElimApp_mkElimApp(x_5, x_1, x_35, x_11, x_12, x_13, x_14, x_49, x_16, x_36);
+if (lean_obj_tag(x_50) == 0)
+{
+lean_object* x_51; lean_object* x_52; lean_object* x_53; lean_object* x_54; lean_object* x_80; lean_object* x_81; lean_object* x_82; lean_object* x_83; lean_object* x_84; lean_object* x_85; lean_object* x_86; lean_object* x_87; lean_object* x_88; uint8_t x_89; 
+x_51 = lean_ctor_get(x_50, 0);
+lean_inc(x_51);
+x_52 = lean_ctor_get(x_50, 1);
+lean_inc(x_52);
+lean_dec(x_50);
+x_53 = lean_ctor_get(x_51, 0);
+lean_inc(x_53);
+x_80 = lean_unsigned_to_nat(0u);
+x_81 = l___private_Lean_Expr_0__Lean_Expr_getAppNumArgsAux(x_53, x_80);
+x_82 = l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___closed__1;
+lean_inc(x_81);
+x_83 = lean_mk_array(x_81, x_82);
+x_84 = lean_unsigned_to_nat(1u);
+x_85 = lean_nat_sub(x_81, x_84);
+lean_dec(x_81);
+lean_inc(x_53);
+x_86 = l___private_Lean_Expr_0__Lean_Expr_getAppArgsAux(x_53, x_83, x_85);
+x_87 = lean_ctor_get(x_5, 1);
+lean_inc(x_87);
+x_88 = lean_array_get_size(x_86);
+x_89 = lean_nat_dec_lt(x_87, x_88);
+lean_dec(x_88);
+if (x_89 == 0)
+{
+lean_object* x_90; lean_object* x_91; 
+lean_dec(x_87);
+lean_dec(x_86);
+x_90 = l_Lean_instInhabitedExpr;
+x_91 = l___private_Init_Util_0__outOfBounds___rarg(x_90);
+x_54 = x_91;
+goto block_79;
+}
+else
+{
+lean_object* x_92; 
+x_92 = lean_array_fget(x_86, x_87);
+lean_dec(x_87);
+lean_dec(x_86);
+x_54 = x_92;
+goto block_79;
+}
+block_79:
+{
+lean_object* x_55; lean_object* x_56; 
+x_55 = l_Lean_Expr_mvarId_x21(x_54);
+lean_inc(x_16);
+lean_inc(x_15);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_6);
+lean_inc(x_33);
+x_56 = l_Lean_Elab_Tactic_ElimApp_setMotiveArg(x_33, x_55, x_6, x_13, x_14, x_15, x_16, x_52);
+if (lean_obj_tag(x_56) == 0)
+{
+lean_object* x_57; lean_object* x_58; lean_object* x_59; lean_object* x_60; lean_object* x_61; lean_object* x_62; lean_object* x_63; 
+x_57 = lean_ctor_get(x_56, 1);
+lean_inc(x_57);
+lean_dec(x_56);
+x_58 = l_Lean_MVarId_assign___at_Lean_Elab_Tactic_closeMainGoal___spec__1(x_33, x_53, x_9, x_10, x_11, x_12, x_13, x_14, x_15, x_16, x_57);
+x_59 = lean_ctor_get(x_58, 1);
+lean_inc(x_59);
+lean_dec(x_58);
+x_60 = lean_ctor_get(x_51, 1);
+lean_inc(x_60);
+x_61 = lean_array_get_size(x_32);
+lean_dec(x_32);
+x_62 = lean_unsigned_to_nat(0u);
+lean_inc(x_16);
+lean_inc(x_15);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_11);
+x_63 = l_Lean_Parser_Tactic_ElimApp_evalNames(x_5, x_60, x_7, x_62, x_61, x_6, x_11, x_12, x_13, x_14, x_15, x_16, x_59);
+lean_dec(x_6);
+lean_dec(x_60);
+if (lean_obj_tag(x_63) == 0)
+{
+lean_object* x_64; lean_object* x_65; lean_object* x_66; lean_object* x_67; lean_object* x_68; lean_object* x_69; lean_object* x_70; 
+x_64 = lean_ctor_get(x_63, 0);
+lean_inc(x_64);
+x_65 = lean_ctor_get(x_63, 1);
+lean_inc(x_65);
+lean_dec(x_63);
+x_66 = lean_ctor_get(x_51, 2);
+lean_inc(x_66);
+lean_dec(x_51);
+x_67 = l_Array_append___rarg(x_64, x_66);
+x_68 = lean_array_to_list(lean_box(0), x_67);
+x_69 = l_List_appendTR___rarg(x_68, x_8);
+x_70 = l_Lean_Elab_Tactic_setGoals(x_69, x_9, x_10, x_11, x_12, x_13, x_14, x_15, x_16, x_65);
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+return x_70;
+}
+else
+{
+uint8_t x_71; 
+lean_dec(x_51);
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_8);
+x_71 = !lean_is_exclusive(x_63);
+if (x_71 == 0)
+{
+return x_63;
+}
+else
+{
+lean_object* x_72; lean_object* x_73; lean_object* x_74; 
+x_72 = lean_ctor_get(x_63, 0);
+x_73 = lean_ctor_get(x_63, 1);
+lean_inc(x_73);
+lean_inc(x_72);
+lean_dec(x_63);
+x_74 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_74, 0, x_72);
+lean_ctor_set(x_74, 1, x_73);
+return x_74;
+}
+}
+}
+else
+{
+uint8_t x_75; 
+lean_dec(x_53);
+lean_dec(x_51);
+lean_dec(x_33);
+lean_dec(x_32);
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_8);
+lean_dec(x_6);
+lean_dec(x_5);
+x_75 = !lean_is_exclusive(x_56);
+if (x_75 == 0)
+{
+return x_56;
+}
+else
+{
+lean_object* x_76; lean_object* x_77; lean_object* x_78; 
+x_76 = lean_ctor_get(x_56, 0);
+x_77 = lean_ctor_get(x_56, 1);
+lean_inc(x_77);
+lean_inc(x_76);
+lean_dec(x_56);
+x_78 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_78, 0, x_76);
+lean_ctor_set(x_78, 1, x_77);
+return x_78;
+}
+}
+}
+}
+else
+{
+uint8_t x_93; 
+lean_dec(x_33);
+lean_dec(x_32);
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_8);
+lean_dec(x_6);
+lean_dec(x_5);
+x_93 = !lean_is_exclusive(x_50);
+if (x_93 == 0)
+{
+return x_50;
+}
+else
+{
+lean_object* x_94; lean_object* x_95; lean_object* x_96; 
+x_94 = lean_ctor_get(x_50, 0);
+x_95 = lean_ctor_get(x_50, 1);
+lean_inc(x_95);
+lean_inc(x_94);
+lean_dec(x_50);
+x_96 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_96, 0, x_94);
+lean_ctor_set(x_96, 1, x_95);
+return x_96;
+}
+}
+}
+else
+{
+uint8_t x_97; 
+lean_dec(x_33);
+lean_dec(x_32);
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_8);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_1);
+x_97 = !lean_is_exclusive(x_34);
+if (x_97 == 0)
+{
+return x_34;
+}
+else
+{
+lean_object* x_98; lean_object* x_99; lean_object* x_100; 
+x_98 = lean_ctor_get(x_34, 0);
+x_99 = lean_ctor_get(x_34, 1);
+lean_inc(x_99);
+lean_inc(x_98);
+lean_dec(x_34);
+x_100 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_100, 0, x_98);
+lean_ctor_set(x_100, 1, x_99);
+return x_100;
+}
+}
+}
+else
+{
+uint8_t x_101; 
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_8);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_1);
+x_101 = !lean_is_exclusive(x_29);
+if (x_101 == 0)
+{
+return x_29;
+}
+else
+{
+lean_object* x_102; lean_object* x_103; lean_object* x_104; 
+x_102 = lean_ctor_get(x_29, 0);
+x_103 = lean_ctor_get(x_29, 1);
+lean_inc(x_103);
+lean_inc(x_102);
+lean_dec(x_29);
+x_104 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_104, 0, x_102);
+lean_ctor_set(x_104, 1, x_103);
+return x_104;
+}
+}
+}
+else
+{
+uint8_t x_105; 
+lean_dec(x_16);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_8);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_3);
+lean_dec(x_1);
+x_105 = !lean_is_exclusive(x_18);
+if (x_105 == 0)
+{
+return x_18;
+}
+else
+{
+lean_object* x_106; lean_object* x_107; lean_object* x_108; 
+x_106 = lean_ctor_get(x_18, 0);
+x_107 = lean_ctor_get(x_18, 1);
+lean_inc(x_107);
+lean_inc(x_106);
+lean_dec(x_18);
+x_108 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_108, 0, x_106);
+lean_ctor_set(x_108, 1, x_107);
+return x_108;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__2(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10, lean_object* x_11, lean_object* x_12, lean_object* x_13, lean_object* x_14, lean_object* x_15, lean_object* x_16) {
+_start:
+{
+lean_object* x_17; 
+lean_inc(x_15);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+x_17 = l_Lean_Meta_getElimInfo(x_1, x_2, x_12, x_13, x_14, x_15, x_16);
+if (lean_obj_tag(x_17) == 0)
+{
+lean_object* x_18; lean_object* x_19; lean_object* x_20; 
+x_18 = lean_ctor_get(x_17, 0);
+lean_inc(x_18);
+x_19 = lean_ctor_get(x_17, 1);
+lean_inc(x_19);
+lean_dec(x_17);
+lean_inc(x_15);
+lean_inc(x_14);
+lean_inc(x_13);
+lean_inc(x_12);
+lean_inc(x_18);
+x_20 = l_Lean_Meta_addImplicitTargets(x_18, x_3, x_12, x_13, x_14, x_15, x_19);
+if (lean_obj_tag(x_20) == 0)
+{
+lean_object* x_21; lean_object* x_22; lean_object* x_23; 
+x_21 = lean_ctor_get(x_20, 0);
+lean_inc(x_21);
+x_22 = lean_ctor_get(x_20, 1);
+lean_inc(x_22);
+lean_dec(x_20);
+x_23 = l_Lean_Elab_Tactic_evalInduction_checkTargets(x_21, x_12, x_13, x_14, x_15, x_22);
+if (lean_obj_tag(x_23) == 0)
+{
+lean_object* x_24; lean_object* x_25; size_t x_26; size_t x_27; lean_object* x_28; lean_object* x_29; lean_object* x_30; lean_object* x_31; 
+x_24 = lean_ctor_get(x_23, 1);
+lean_inc(x_24);
+lean_dec(x_23);
+x_25 = lean_array_get_size(x_21);
+x_26 = lean_usize_of_nat(x_25);
+lean_dec(x_25);
+x_27 = 0;
+lean_inc(x_21);
+x_28 = l_Array_mapMUnsafe_map___at_Lean_Elab_Tactic_evalInduction___spec__2(x_26, x_27, x_21);
+x_29 = lean_box(0);
+lean_inc(x_4);
+x_30 = lean_alloc_closure((void*)(l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___boxed), 17, 8);
+lean_closure_set(x_30, 0, x_21);
+lean_closure_set(x_30, 1, x_29);
+lean_closure_set(x_30, 2, x_4);
+lean_closure_set(x_30, 3, x_5);
+lean_closure_set(x_30, 4, x_18);
+lean_closure_set(x_30, 5, x_28);
+lean_closure_set(x_30, 6, x_6);
+lean_closure_set(x_30, 7, x_7);
+x_31 = l_Lean_MVarId_withContext___at_Lean_Elab_Tactic_withMainContext___spec__1___rarg(x_4, x_30, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15, x_24);
+return x_31;
+}
+else
+{
+uint8_t x_32; 
+lean_dec(x_21);
+lean_dec(x_18);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+x_32 = !lean_is_exclusive(x_23);
+if (x_32 == 0)
+{
+return x_23;
+}
+else
+{
+lean_object* x_33; lean_object* x_34; lean_object* x_35; 
+x_33 = lean_ctor_get(x_23, 0);
+x_34 = lean_ctor_get(x_23, 1);
+lean_inc(x_34);
+lean_inc(x_33);
+lean_dec(x_23);
+x_35 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_35, 0, x_33);
+lean_ctor_set(x_35, 1, x_34);
+return x_35;
+}
+}
+}
+else
+{
+uint8_t x_36; 
+lean_dec(x_18);
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+x_36 = !lean_is_exclusive(x_20);
+if (x_36 == 0)
+{
+return x_20;
+}
+else
+{
+lean_object* x_37; lean_object* x_38; lean_object* x_39; 
+x_37 = lean_ctor_get(x_20, 0);
+x_38 = lean_ctor_get(x_20, 1);
+lean_inc(x_38);
+lean_inc(x_37);
+lean_dec(x_20);
+x_39 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_39, 0, x_37);
+lean_ctor_set(x_39, 1, x_38);
+return x_39;
+}
+}
+}
+else
+{
+uint8_t x_40; 
+lean_dec(x_15);
+lean_dec(x_14);
+lean_dec(x_13);
+lean_dec(x_12);
+lean_dec(x_11);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+x_40 = !lean_is_exclusive(x_17);
+if (x_40 == 0)
+{
+return x_17;
+}
+else
+{
+lean_object* x_41; lean_object* x_42; lean_object* x_43; 
+x_41 = lean_ctor_get(x_17, 0);
+x_42 = lean_ctor_get(x_17, 1);
+lean_inc(x_42);
+lean_inc(x_41);
+lean_dec(x_17);
+x_43 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_43, 0, x_41);
+lean_ctor_set(x_43, 1, x_42);
+return x_43;
+}
+}
+}
+}
+static lean_object* _init_l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("rec'", 4);
+return x_1;
+}
+}
+static lean_object* _init_l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__1;
+x_2 = l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__1;
+x_3 = l_Lean_Name_mkStr2(x_1, x_2);
+return x_3;
+}
+}
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9, lean_object* x_10) {
+_start:
+{
+lean_object* x_11; uint8_t x_12; 
+x_11 = l_MyNat_induction___closed__4;
+lean_inc(x_1);
+x_12 = l_Lean_Syntax_isOfKind(x_1, x_11);
+if (x_12 == 0)
+{
+lean_object* x_13; 
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_13 = l_Lean_Elab_throwUnsupportedSyntax___at_Std_Tactic___aux__Std__Tactic__ShowTerm______elabRules__Std__Tactic__showTermTac__1___spec__1___rarg(x_10);
+return x_13;
+}
+else
+{
+lean_object* x_14; lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; lean_object* x_19; 
+x_14 = lean_unsigned_to_nat(1u);
+x_15 = l_Lean_Syntax_getArg(x_1, x_14);
+x_16 = lean_unsigned_to_nat(2u);
+x_17 = l_Lean_Syntax_getArg(x_1, x_16);
+lean_dec(x_1);
+x_18 = l_Lean_Syntax_getSepArgs(x_15);
+lean_inc(x_9);
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_6);
+lean_inc(x_5);
+lean_inc(x_4);
+lean_inc(x_3);
+lean_inc(x_2);
+x_19 = l_Lean_Elab_Tactic_elabCasesTargets(x_18, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10);
+if (lean_obj_tag(x_19) == 0)
+{
+lean_object* x_20; lean_object* x_21; lean_object* x_22; lean_object* x_23; 
+x_20 = lean_ctor_get(x_19, 0);
+lean_inc(x_20);
+x_21 = lean_ctor_get(x_19, 1);
+lean_inc(x_21);
+lean_dec(x_19);
+x_22 = l_Lean_Elab_Tactic_getUnsolvedGoals(x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_21);
+x_23 = lean_ctor_get(x_22, 0);
+lean_inc(x_23);
+if (lean_obj_tag(x_23) == 0)
+{
+lean_object* x_24; lean_object* x_25; 
+lean_dec(x_20);
+lean_dec(x_17);
+lean_dec(x_15);
+x_24 = lean_ctor_get(x_22, 1);
+lean_inc(x_24);
+lean_dec(x_22);
+x_25 = l_Lean_Elab_Tactic_throwNoGoalsToBeSolved___rarg(x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_24);
+return x_25;
+}
+else
+{
+lean_object* x_26; lean_object* x_27; lean_object* x_28; lean_object* x_29; lean_object* x_30; lean_object* x_31; lean_object* x_32; 
+x_26 = lean_ctor_get(x_22, 1);
+lean_inc(x_26);
+lean_dec(x_22);
+x_27 = lean_ctor_get(x_23, 0);
+lean_inc(x_27);
+x_28 = lean_ctor_get(x_23, 1);
+lean_inc(x_28);
+lean_dec(x_23);
+x_29 = lean_box(0);
+x_30 = l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__2;
+lean_inc(x_27);
+x_31 = lean_alloc_closure((void*)(l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__2), 16, 7);
+lean_closure_set(x_31, 0, x_30);
+lean_closure_set(x_31, 1, x_29);
+lean_closure_set(x_31, 2, x_20);
+lean_closure_set(x_31, 3, x_27);
+lean_closure_set(x_31, 4, x_15);
+lean_closure_set(x_31, 5, x_17);
+lean_closure_set(x_31, 6, x_28);
+x_32 = l_Lean_MVarId_withContext___at_Lean_Elab_Tactic_withMainContext___spec__1___rarg(x_27, x_31, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_26);
+return x_32;
+}
+}
+else
+{
+uint8_t x_33; 
+lean_dec(x_17);
+lean_dec(x_15);
+lean_dec(x_9);
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+x_33 = !lean_is_exclusive(x_19);
+if (x_33 == 0)
+{
+return x_19;
+}
+else
+{
+lean_object* x_34; lean_object* x_35; lean_object* x_36; 
+x_34 = lean_ctor_get(x_19, 0);
+x_35 = lean_ctor_get(x_19, 1);
+lean_inc(x_35);
+lean_inc(x_34);
+lean_dec(x_19);
+x_36 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_36, 0, x_34);
+lean_ctor_set(x_36, 1, x_35);
+return x_36;
+}
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___boxed(lean_object** _args) {
+lean_object* x_1 = _args[0];
+lean_object* x_2 = _args[1];
+lean_object* x_3 = _args[2];
+lean_object* x_4 = _args[3];
+lean_object* x_5 = _args[4];
+lean_object* x_6 = _args[5];
+lean_object* x_7 = _args[6];
+lean_object* x_8 = _args[7];
+lean_object* x_9 = _args[8];
+lean_object* x_10 = _args[9];
+lean_object* x_11 = _args[10];
+lean_object* x_12 = _args[11];
+lean_object* x_13 = _args[12];
+lean_object* x_14 = _args[13];
+lean_object* x_15 = _args[14];
+lean_object* x_16 = _args[15];
+lean_object* x_17 = _args[16];
+_start:
+{
+lean_object* x_18; 
+x_18 = l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15, x_16, x_17);
+lean_dec(x_10);
+lean_dec(x_9);
+lean_dec(x_7);
+lean_dec(x_4);
+return x_18;
+}
+}
+static lean_object* _init_l_MyNat_rfl___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("rfl", 3);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_rfl___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l_MyNat_rewriteSeq___closed__1;
+x_2 = l_MyNat_rfl___closed__1;
+x_3 = l_Lean_Name_mkStr2(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rfl___closed__3() {
+_start:
+{
+lean_object* x_1; uint8_t x_2; lean_object* x_3; 
+x_1 = l_MyNat_rfl___closed__1;
+x_2 = 0;
+x_3 = lean_alloc_ctor(6, 1, 1);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set_uint8(x_3, sizeof(void*)*1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_rfl___closed__4() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_MyNat_rfl___closed__2;
+x_2 = lean_unsigned_to_nat(1024u);
+x_3 = l_MyNat_rfl___closed__3;
+x_4 = lean_alloc_ctor(3, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_rfl() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_MyNat_rfl___closed__4;
+return x_1;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRfl___rarg___lambda__1(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9) {
+_start:
+{
+lean_object* x_10; 
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_6);
+lean_inc(x_5);
+lean_inc(x_4);
+lean_inc(x_3);
+lean_inc(x_2);
+lean_inc(x_1);
+x_10 = l_Lean_Elab_Tactic_getMainGoal(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9);
+if (lean_obj_tag(x_10) == 0)
+{
+lean_object* x_11; lean_object* x_12; lean_object* x_13; lean_object* x_14; lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; uint8_t x_19; 
+x_11 = lean_ctor_get(x_5, 0);
+lean_inc(x_11);
+x_12 = lean_ctor_get(x_10, 0);
+lean_inc(x_12);
+x_13 = lean_ctor_get(x_10, 1);
+lean_inc(x_13);
+lean_dec(x_10);
+x_14 = lean_ctor_get(x_5, 1);
+lean_inc(x_14);
+x_15 = lean_ctor_get(x_5, 2);
+lean_inc(x_15);
+x_16 = lean_ctor_get(x_5, 3);
+lean_inc(x_16);
+x_17 = lean_ctor_get(x_5, 4);
+lean_inc(x_17);
+x_18 = lean_ctor_get(x_5, 5);
+lean_inc(x_18);
+x_19 = !lean_is_exclusive(x_11);
+if (x_19 == 0)
+{
+uint8_t x_20; lean_object* x_21; lean_object* x_22; 
+x_20 = 2;
+lean_ctor_set_uint8(x_11, 5, x_20);
+x_21 = lean_alloc_ctor(0, 6, 0);
+lean_ctor_set(x_21, 0, x_11);
+lean_ctor_set(x_21, 1, x_14);
+lean_ctor_set(x_21, 2, x_15);
+lean_ctor_set(x_21, 3, x_16);
+lean_ctor_set(x_21, 4, x_17);
+lean_ctor_set(x_21, 5, x_18);
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_6);
+x_22 = l_Lean_MVarId_refl(x_12, x_21, x_6, x_7, x_8, x_13);
+if (lean_obj_tag(x_22) == 0)
+{
+lean_object* x_23; lean_object* x_24; lean_object* x_25; 
+x_23 = lean_ctor_get(x_22, 1);
+lean_inc(x_23);
+lean_dec(x_22);
+x_24 = lean_box(0);
+x_25 = l_Lean_Elab_Tactic_replaceMainGoal(x_24, x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_23);
+if (lean_obj_tag(x_25) == 0)
+{
+uint8_t x_26; 
+x_26 = !lean_is_exclusive(x_25);
+if (x_26 == 0)
+{
+lean_object* x_27; lean_object* x_28; 
+x_27 = lean_ctor_get(x_25, 0);
+lean_dec(x_27);
+x_28 = lean_box(0);
+lean_ctor_set(x_25, 0, x_28);
+return x_25;
+}
+else
+{
+lean_object* x_29; lean_object* x_30; lean_object* x_31; 
+x_29 = lean_ctor_get(x_25, 1);
+lean_inc(x_29);
+lean_dec(x_25);
+x_30 = lean_box(0);
+x_31 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_31, 0, x_30);
+lean_ctor_set(x_31, 1, x_29);
+return x_31;
+}
+}
+else
+{
+uint8_t x_32; 
+x_32 = !lean_is_exclusive(x_25);
+if (x_32 == 0)
+{
+return x_25;
+}
+else
+{
+lean_object* x_33; lean_object* x_34; lean_object* x_35; 
+x_33 = lean_ctor_get(x_25, 0);
+x_34 = lean_ctor_get(x_25, 1);
+lean_inc(x_34);
+lean_inc(x_33);
+lean_dec(x_25);
+x_35 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_35, 0, x_33);
+lean_ctor_set(x_35, 1, x_34);
+return x_35;
+}
+}
+}
+else
+{
+uint8_t x_36; 
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_36 = !lean_is_exclusive(x_22);
+if (x_36 == 0)
+{
+return x_22;
+}
+else
+{
+lean_object* x_37; lean_object* x_38; lean_object* x_39; 
+x_37 = lean_ctor_get(x_22, 0);
+x_38 = lean_ctor_get(x_22, 1);
+lean_inc(x_38);
+lean_inc(x_37);
+lean_dec(x_22);
+x_39 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_39, 0, x_37);
+lean_ctor_set(x_39, 1, x_38);
+return x_39;
+}
+}
+}
+else
+{
+uint8_t x_40; uint8_t x_41; uint8_t x_42; uint8_t x_43; uint8_t x_44; uint8_t x_45; uint8_t x_46; uint8_t x_47; uint8_t x_48; uint8_t x_49; uint8_t x_50; uint8_t x_51; uint8_t x_52; lean_object* x_53; lean_object* x_54; lean_object* x_55; 
+x_40 = lean_ctor_get_uint8(x_11, 0);
+x_41 = lean_ctor_get_uint8(x_11, 1);
+x_42 = lean_ctor_get_uint8(x_11, 2);
+x_43 = lean_ctor_get_uint8(x_11, 3);
+x_44 = lean_ctor_get_uint8(x_11, 4);
+x_45 = lean_ctor_get_uint8(x_11, 6);
+x_46 = lean_ctor_get_uint8(x_11, 7);
+x_47 = lean_ctor_get_uint8(x_11, 8);
+x_48 = lean_ctor_get_uint8(x_11, 9);
+x_49 = lean_ctor_get_uint8(x_11, 10);
+x_50 = lean_ctor_get_uint8(x_11, 11);
+x_51 = lean_ctor_get_uint8(x_11, 12);
+lean_dec(x_11);
+x_52 = 2;
+x_53 = lean_alloc_ctor(0, 0, 13);
+lean_ctor_set_uint8(x_53, 0, x_40);
+lean_ctor_set_uint8(x_53, 1, x_41);
+lean_ctor_set_uint8(x_53, 2, x_42);
+lean_ctor_set_uint8(x_53, 3, x_43);
+lean_ctor_set_uint8(x_53, 4, x_44);
+lean_ctor_set_uint8(x_53, 5, x_52);
+lean_ctor_set_uint8(x_53, 6, x_45);
+lean_ctor_set_uint8(x_53, 7, x_46);
+lean_ctor_set_uint8(x_53, 8, x_47);
+lean_ctor_set_uint8(x_53, 9, x_48);
+lean_ctor_set_uint8(x_53, 10, x_49);
+lean_ctor_set_uint8(x_53, 11, x_50);
+lean_ctor_set_uint8(x_53, 12, x_51);
+x_54 = lean_alloc_ctor(0, 6, 0);
+lean_ctor_set(x_54, 0, x_53);
+lean_ctor_set(x_54, 1, x_14);
+lean_ctor_set(x_54, 2, x_15);
+lean_ctor_set(x_54, 3, x_16);
+lean_ctor_set(x_54, 4, x_17);
+lean_ctor_set(x_54, 5, x_18);
+lean_inc(x_8);
+lean_inc(x_7);
+lean_inc(x_6);
+x_55 = l_Lean_MVarId_refl(x_12, x_54, x_6, x_7, x_8, x_13);
+if (lean_obj_tag(x_55) == 0)
+{
+lean_object* x_56; lean_object* x_57; lean_object* x_58; 
+x_56 = lean_ctor_get(x_55, 1);
+lean_inc(x_56);
+lean_dec(x_55);
+x_57 = lean_box(0);
+x_58 = l_Lean_Elab_Tactic_replaceMainGoal(x_57, x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_56);
+if (lean_obj_tag(x_58) == 0)
+{
+lean_object* x_59; lean_object* x_60; lean_object* x_61; lean_object* x_62; 
+x_59 = lean_ctor_get(x_58, 1);
+lean_inc(x_59);
+if (lean_is_exclusive(x_58)) {
+ lean_ctor_release(x_58, 0);
+ lean_ctor_release(x_58, 1);
+ x_60 = x_58;
+} else {
+ lean_dec_ref(x_58);
+ x_60 = lean_box(0);
+}
+x_61 = lean_box(0);
+if (lean_is_scalar(x_60)) {
+ x_62 = lean_alloc_ctor(0, 2, 0);
+} else {
+ x_62 = x_60;
+}
+lean_ctor_set(x_62, 0, x_61);
+lean_ctor_set(x_62, 1, x_59);
+return x_62;
+}
+else
+{
+lean_object* x_63; lean_object* x_64; lean_object* x_65; lean_object* x_66; 
+x_63 = lean_ctor_get(x_58, 0);
+lean_inc(x_63);
+x_64 = lean_ctor_get(x_58, 1);
+lean_inc(x_64);
+if (lean_is_exclusive(x_58)) {
+ lean_ctor_release(x_58, 0);
+ lean_ctor_release(x_58, 1);
+ x_65 = x_58;
+} else {
+ lean_dec_ref(x_58);
+ x_65 = lean_box(0);
+}
+if (lean_is_scalar(x_65)) {
+ x_66 = lean_alloc_ctor(1, 2, 0);
+} else {
+ x_66 = x_65;
+}
+lean_ctor_set(x_66, 0, x_63);
+lean_ctor_set(x_66, 1, x_64);
+return x_66;
+}
+}
+else
+{
+lean_object* x_67; lean_object* x_68; lean_object* x_69; lean_object* x_70; 
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_67 = lean_ctor_get(x_55, 0);
+lean_inc(x_67);
+x_68 = lean_ctor_get(x_55, 1);
+lean_inc(x_68);
+if (lean_is_exclusive(x_55)) {
+ lean_ctor_release(x_55, 0);
+ lean_ctor_release(x_55, 1);
+ x_69 = x_55;
+} else {
+ lean_dec_ref(x_55);
+ x_69 = lean_box(0);
+}
+if (lean_is_scalar(x_69)) {
+ x_70 = lean_alloc_ctor(1, 2, 0);
+} else {
+ x_70 = x_69;
+}
+lean_ctor_set(x_70, 0, x_67);
+lean_ctor_set(x_70, 1, x_68);
+return x_70;
+}
+}
+}
+else
+{
+uint8_t x_71; 
+lean_dec(x_8);
+lean_dec(x_7);
+lean_dec(x_6);
+lean_dec(x_5);
+lean_dec(x_4);
+lean_dec(x_3);
+lean_dec(x_2);
+lean_dec(x_1);
+x_71 = !lean_is_exclusive(x_10);
+if (x_71 == 0)
+{
+return x_10;
+}
+else
+{
+lean_object* x_72; lean_object* x_73; lean_object* x_74; 
+x_72 = lean_ctor_get(x_10, 0);
+x_73 = lean_ctor_get(x_10, 1);
+lean_inc(x_73);
+lean_inc(x_72);
+lean_dec(x_10);
+x_74 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_74, 0, x_72);
+lean_ctor_set(x_74, 1, x_73);
+return x_74;
+}
+}
+}
+}
+static lean_object* _init_l_MyNat_evalRfl___rarg___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_alloc_closure((void*)(l_MyNat_evalRfl___rarg___lambda__1), 9, 0);
+return x_1;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRfl___rarg(lean_object* x_1, lean_object* x_2, lean_object* x_3, lean_object* x_4, lean_object* x_5, lean_object* x_6, lean_object* x_7, lean_object* x_8, lean_object* x_9) {
+_start:
+{
+lean_object* x_10; lean_object* x_11; 
+x_10 = l_MyNat_evalRfl___rarg___closed__1;
+x_11 = l_Lean_Elab_Tactic_withMainContext___rarg(x_10, x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9);
+return x_11;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRfl(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = lean_alloc_closure((void*)(l_MyNat_evalRfl___rarg), 9, 0);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_evalRfl___boxed(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = l_MyNat_evalRfl(x_1);
+lean_dec(x_1);
+return x_2;
+}
+}
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_Mathlib_Lean_Expr_Basic(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+lean_object* initialize_Lean_Elab_Tactic_Basic(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_Modifications_Tactics(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Mathlib_Lean_Expr_Basic(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_Lean_Elab_Tactic_Basic(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+l_MyNat_rewriteSeq___closed__1 = _init_l_MyNat_rewriteSeq___closed__1();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__1);
+l_MyNat_rewriteSeq___closed__2 = _init_l_MyNat_rewriteSeq___closed__2();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__2);
+l_MyNat_rewriteSeq___closed__3 = _init_l_MyNat_rewriteSeq___closed__3();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__3);
+l_MyNat_rewriteSeq___closed__4 = _init_l_MyNat_rewriteSeq___closed__4();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__4);
+l_MyNat_rewriteSeq___closed__5 = _init_l_MyNat_rewriteSeq___closed__5();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__5);
+l_MyNat_rewriteSeq___closed__6 = _init_l_MyNat_rewriteSeq___closed__6();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__6);
+l_MyNat_rewriteSeq___closed__7 = _init_l_MyNat_rewriteSeq___closed__7();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__7);
+l_MyNat_rewriteSeq___closed__8 = _init_l_MyNat_rewriteSeq___closed__8();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__8);
+l_MyNat_rewriteSeq___closed__9 = _init_l_MyNat_rewriteSeq___closed__9();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__9);
+l_MyNat_rewriteSeq___closed__10 = _init_l_MyNat_rewriteSeq___closed__10();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__10);
+l_MyNat_rewriteSeq___closed__11 = _init_l_MyNat_rewriteSeq___closed__11();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__11);
+l_MyNat_rewriteSeq___closed__12 = _init_l_MyNat_rewriteSeq___closed__12();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__12);
+l_MyNat_rewriteSeq___closed__13 = _init_l_MyNat_rewriteSeq___closed__13();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__13);
+l_MyNat_rewriteSeq___closed__14 = _init_l_MyNat_rewriteSeq___closed__14();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__14);
+l_MyNat_rewriteSeq___closed__15 = _init_l_MyNat_rewriteSeq___closed__15();
+lean_mark_persistent(l_MyNat_rewriteSeq___closed__15);
+l_MyNat_rewriteSeq = _init_l_MyNat_rewriteSeq();
+lean_mark_persistent(l_MyNat_rewriteSeq);
+l_MyNat_evalRewriteSeq___lambda__2___closed__1 = _init_l_MyNat_evalRewriteSeq___lambda__2___closed__1();
+lean_mark_persistent(l_MyNat_evalRewriteSeq___lambda__2___closed__1);
+l_MyNat_evalRewriteSeq___lambda__2___closed__2 = _init_l_MyNat_evalRewriteSeq___lambda__2___closed__2();
+lean_mark_persistent(l_MyNat_evalRewriteSeq___lambda__2___closed__2);
+l_MyNat_evalRewriteSeq___lambda__2___closed__3 = _init_l_MyNat_evalRewriteSeq___lambda__2___closed__3();
+lean_mark_persistent(l_MyNat_evalRewriteSeq___lambda__2___closed__3);
+l_MyNat_evalRewriteSeq___lambda__2___closed__4 = _init_l_MyNat_evalRewriteSeq___lambda__2___closed__4();
+lean_mark_persistent(l_MyNat_evalRewriteSeq___lambda__2___closed__4);
+l_MyNat_evalRewriteSeq___lambda__2___closed__5 = _init_l_MyNat_evalRewriteSeq___lambda__2___closed__5();
+lean_mark_persistent(l_MyNat_evalRewriteSeq___lambda__2___closed__5);
+l_MyNat_evalRewriteSeq___lambda__3___closed__1 = _init_l_MyNat_evalRewriteSeq___lambda__3___closed__1();
+lean_mark_persistent(l_MyNat_evalRewriteSeq___lambda__3___closed__1);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__1);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__2);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__3);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__4 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__4();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__4);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__5 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__5();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__5);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__6 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__6();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__6);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__7 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__7();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__7);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__8 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__8();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__8);
+l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__9 = _init_l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__9();
+lean_mark_persistent(l_Array_forInUnsafe_loop___at_Lean_Parser_Tactic_ElimApp_evalNames___spec__4___closed__9);
+l_Lean_Parser_Tactic_ElimApp_evalNames___closed__1 = _init_l_Lean_Parser_Tactic_ElimApp_evalNames___closed__1();
+lean_mark_persistent(l_Lean_Parser_Tactic_ElimApp_evalNames___closed__1);
+l_MyNat_induction___closed__1 = _init_l_MyNat_induction___closed__1();
+lean_mark_persistent(l_MyNat_induction___closed__1);
+l_MyNat_induction___closed__2 = _init_l_MyNat_induction___closed__2();
+lean_mark_persistent(l_MyNat_induction___closed__2);
+l_MyNat_induction___closed__3 = _init_l_MyNat_induction___closed__3();
+lean_mark_persistent(l_MyNat_induction___closed__3);
+l_MyNat_induction___closed__4 = _init_l_MyNat_induction___closed__4();
+lean_mark_persistent(l_MyNat_induction___closed__4);
+l_MyNat_induction___closed__5 = _init_l_MyNat_induction___closed__5();
+lean_mark_persistent(l_MyNat_induction___closed__5);
+l_MyNat_induction___closed__6 = _init_l_MyNat_induction___closed__6();
+lean_mark_persistent(l_MyNat_induction___closed__6);
+l_MyNat_induction___closed__7 = _init_l_MyNat_induction___closed__7();
+lean_mark_persistent(l_MyNat_induction___closed__7);
+l_MyNat_induction___closed__8 = _init_l_MyNat_induction___closed__8();
+lean_mark_persistent(l_MyNat_induction___closed__8);
+l_MyNat_induction___closed__9 = _init_l_MyNat_induction___closed__9();
+lean_mark_persistent(l_MyNat_induction___closed__9);
+l_MyNat_induction___closed__10 = _init_l_MyNat_induction___closed__10();
+lean_mark_persistent(l_MyNat_induction___closed__10);
+l_MyNat_induction___closed__11 = _init_l_MyNat_induction___closed__11();
+lean_mark_persistent(l_MyNat_induction___closed__11);
+l_MyNat_induction___closed__12 = _init_l_MyNat_induction___closed__12();
+lean_mark_persistent(l_MyNat_induction___closed__12);
+l_MyNat_induction___closed__13 = _init_l_MyNat_induction___closed__13();
+lean_mark_persistent(l_MyNat_induction___closed__13);
+l_MyNat_induction___closed__14 = _init_l_MyNat_induction___closed__14();
+lean_mark_persistent(l_MyNat_induction___closed__14);
+l_MyNat_induction___closed__15 = _init_l_MyNat_induction___closed__15();
+lean_mark_persistent(l_MyNat_induction___closed__15);
+l_MyNat_induction___closed__16 = _init_l_MyNat_induction___closed__16();
+lean_mark_persistent(l_MyNat_induction___closed__16);
+l_MyNat_induction___closed__17 = _init_l_MyNat_induction___closed__17();
+lean_mark_persistent(l_MyNat_induction___closed__17);
+l_MyNat_induction___closed__18 = _init_l_MyNat_induction___closed__18();
+lean_mark_persistent(l_MyNat_induction___closed__18);
+l_MyNat_induction___closed__19 = _init_l_MyNat_induction___closed__19();
+lean_mark_persistent(l_MyNat_induction___closed__19);
+l_MyNat_induction___closed__20 = _init_l_MyNat_induction___closed__20();
+lean_mark_persistent(l_MyNat_induction___closed__20);
+l_MyNat_induction___closed__21 = _init_l_MyNat_induction___closed__21();
+lean_mark_persistent(l_MyNat_induction___closed__21);
+l_MyNat_induction___closed__22 = _init_l_MyNat_induction___closed__22();
+lean_mark_persistent(l_MyNat_induction___closed__22);
+l_MyNat_induction___closed__23 = _init_l_MyNat_induction___closed__23();
+lean_mark_persistent(l_MyNat_induction___closed__23);
+l_MyNat_induction___closed__24 = _init_l_MyNat_induction___closed__24();
+lean_mark_persistent(l_MyNat_induction___closed__24);
+l_MyNat_induction = _init_l_MyNat_induction();
+lean_mark_persistent(l_MyNat_induction);
+l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___closed__1 = _init_l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___closed__1();
+lean_mark_persistent(l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___lambda__1___closed__1);
+l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__1 = _init_l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__1();
+lean_mark_persistent(l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__1);
+l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__2 = _init_l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__2();
+lean_mark_persistent(l_Lean_Parser_Tactic___aux__NNG__Modifications__Tactics______elabRules__Lean__Parser__Tactic____root____MyNat__induction__1___closed__2);
+l_MyNat_rfl___closed__1 = _init_l_MyNat_rfl___closed__1();
+lean_mark_persistent(l_MyNat_rfl___closed__1);
+l_MyNat_rfl___closed__2 = _init_l_MyNat_rfl___closed__2();
+lean_mark_persistent(l_MyNat_rfl___closed__2);
+l_MyNat_rfl___closed__3 = _init_l_MyNat_rfl___closed__3();
+lean_mark_persistent(l_MyNat_rfl___closed__3);
+l_MyNat_rfl___closed__4 = _init_l_MyNat_rfl___closed__4();
+lean_mark_persistent(l_MyNat_rfl___closed__4);
+l_MyNat_rfl = _init_l_MyNat_rfl();
+lean_mark_persistent(l_MyNat_rfl);
+l_MyNat_evalRfl___rarg___closed__1 = _init_l_MyNat_evalRfl___rarg___closed__1();
+lean_mark_persistent(l_MyNat_evalRfl___rarg___closed__1);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/Modifications/Tactics.c.trace b/server/nng/build/ir/NNG/Modifications/Tactics.c.trace
new file mode 100644
index 0000000..b8a6417
--- /dev/null
+++ b/server/nng/build/ir/NNG/Modifications/Tactics.c.trace
@@ -0,0 +1 @@
+14754082556322596060
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/MyNat/Addition.c b/server/nng/build/ir/NNG/MyNat/Addition.c
new file mode 100644
index 0000000..db5eec9
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Addition.c
@@ -0,0 +1,100 @@
+// Lean compiler output
+// Module: NNG.MyNat.Addition
+// Imports: Init NNG.MyNat.Definition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+static lean_object* l_MyNat_instAddMyNat___closed__1;
+LEAN_EXPORT lean_object* l_MyNat_add___boxed(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_instAddMyNat;
+LEAN_EXPORT lean_object* l_MyNat_add(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_add(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+if (lean_obj_tag(x_2) == 0)
+{
+lean_inc(x_1);
+return x_1;
+}
+else
+{
+uint8_t x_3; 
+x_3 = !lean_is_exclusive(x_2);
+if (x_3 == 0)
+{
+lean_object* x_4; lean_object* x_5; 
+x_4 = lean_ctor_get(x_2, 0);
+x_5 = l_MyNat_add(x_1, x_4);
+lean_ctor_set(x_2, 0, x_5);
+return x_2;
+}
+else
+{
+lean_object* x_6; lean_object* x_7; lean_object* x_8; 
+x_6 = lean_ctor_get(x_2, 0);
+lean_inc(x_6);
+lean_dec(x_2);
+x_7 = l_MyNat_add(x_1, x_6);
+x_8 = lean_alloc_ctor(1, 1, 0);
+lean_ctor_set(x_8, 0, x_7);
+return x_8;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_add___boxed(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+lean_object* x_3; 
+x_3 = l_MyNat_add(x_1, x_2);
+lean_dec(x_1);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_instAddMyNat___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_alloc_closure((void*)(l_MyNat_add___boxed), 2, 0);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_instAddMyNat() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_MyNat_instAddMyNat___closed__1;
+return x_1;
+}
+}
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Definition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Definition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+l_MyNat_instAddMyNat___closed__1 = _init_l_MyNat_instAddMyNat___closed__1();
+lean_mark_persistent(l_MyNat_instAddMyNat___closed__1);
+l_MyNat_instAddMyNat = _init_l_MyNat_instAddMyNat();
+lean_mark_persistent(l_MyNat_instAddMyNat);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/MyNat/Addition.c.trace b/server/nng/build/ir/NNG/MyNat/Addition.c.trace
new file mode 100644
index 0000000..9a68d6e
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Addition.c.trace
@@ -0,0 +1 @@
+2760095421866741095
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/MyNat/Definition.c b/server/nng/build/ir/NNG/MyNat/Definition.c
new file mode 100644
index 0000000..344c155
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Definition.c
@@ -0,0 +1,799 @@
+// Lean compiler output
+// Module: NNG.MyNat.Definition
+// Imports: Init
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__2;
+LEAN_EXPORT lean_object* l___private_NNG_MyNat_Definition_0__decEqMyNat____x40_NNG_MyNat_Definition___hyg_99____boxed(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_instInhabitedMyNat;
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__10;
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__6;
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__7;
+lean_object* lean_mk_empty_array_with_capacity(lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1;
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__9;
+static lean_object* l_term_u2115___closed__5;
+LEAN_EXPORT lean_object* l_instInhabitedMyNat;
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__3;
+LEAN_EXPORT uint8_t l___private_NNG_MyNat_Definition_0__decEqMyNat____x40_NNG_MyNat_Definition___hyg_99_(lean_object*, lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__4;
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3;
+LEAN_EXPORT lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___boxed(lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Syntax_getArgs(lean_object*);
+static lean_object* l_term_u2115___closed__1;
+lean_object* l_Lean_replaceRef(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_instToStringMyNat___boxed(lean_object*);
+uint8_t l_Lean_Syntax_isOfKind(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_one;
+LEAN_EXPORT lean_object* l___private_NNG_MyNat_Definition_0__beqMyNat____x40_NNG_MyNat_Definition___hyg_15____boxed(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_term_u2115;
+lean_object* l_Lean_SourceInfo_fromRef(lean_object*, uint8_t);
+LEAN_EXPORT lean_object* l_MyNat_ofNat(lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__5;
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__4;
+LEAN_EXPORT lean_object* l_MyNat_myNatFromNat(lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__7;
+LEAN_EXPORT lean_object* l_MyNat_natFromMyNat(lean_object*);
+LEAN_EXPORT uint8_t l___private_NNG_MyNat_Definition_0__beqMyNat____x40_NNG_MyNat_Definition___hyg_15_(lean_object*, lean_object*);
+lean_object* l_Lean_addMacroScope(lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Name_str___override(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_instToStringMyNat(lean_object*);
+lean_object* l_Lean_Syntax_node2(lean_object*, lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Syntax_getArg(lean_object*, lean_object*);
+lean_object* l_Array_append___rarg(lean_object*, lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__8;
+static lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__5;
+static lean_object* l_MyNat_one___closed__2;
+static lean_object* l_MyNat_one___closed__1;
+uint8_t lean_nat_dec_eq(lean_object*, lean_object*);
+static lean_object* l_instBEqMyNat___closed__1;
+lean_object* l_Lean_Syntax_node1(lean_object*, lean_object*, lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__6;
+lean_object* lean_nat_sub(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_myNatFromNat___boxed(lean_object*);
+static lean_object* l_term_u2115___closed__4;
+LEAN_EXPORT lean_object* l_MyNat_natFromMyNat___boxed(lean_object*);
+LEAN_EXPORT lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1(lean_object*, lean_object*, lean_object*);
+lean_object* l_Lean_Name_mkStr4(lean_object*, lean_object*, lean_object*, lean_object*);
+LEAN_EXPORT uint8_t l_instDecidableEqMyNat(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_instDecidableEqMyNat___boxed(lean_object*, lean_object*);
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__1;
+lean_object* lean_nat_add(lean_object*, lean_object*);
+static lean_object* l_term_u2115___closed__3;
+static lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__2;
+LEAN_EXPORT lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1(lean_object*, lean_object*, lean_object*);
+lean_object* l_String_toSubstring_x27(lean_object*);
+lean_object* l_Nat_repr(lean_object*);
+static lean_object* l_term_u2115___closed__2;
+LEAN_EXPORT lean_object* l_instBEqMyNat;
+LEAN_EXPORT lean_object* l_MyNat_ofNat___boxed(lean_object*);
+LEAN_EXPORT uint8_t l___private_NNG_MyNat_Definition_0__beqMyNat____x40_NNG_MyNat_Definition___hyg_15_(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+if (lean_obj_tag(x_1) == 0)
+{
+if (lean_obj_tag(x_2) == 0)
+{
+uint8_t x_3; 
+x_3 = 1;
+return x_3;
+}
+else
+{
+uint8_t x_4; 
+x_4 = 0;
+return x_4;
+}
+}
+else
+{
+if (lean_obj_tag(x_2) == 0)
+{
+uint8_t x_5; 
+x_5 = 0;
+return x_5;
+}
+else
+{
+lean_object* x_6; lean_object* x_7; 
+x_6 = lean_ctor_get(x_1, 0);
+x_7 = lean_ctor_get(x_2, 0);
+x_1 = x_6;
+x_2 = x_7;
+goto _start;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l___private_NNG_MyNat_Definition_0__beqMyNat____x40_NNG_MyNat_Definition___hyg_15____boxed(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+uint8_t x_3; lean_object* x_4; 
+x_3 = l___private_NNG_MyNat_Definition_0__beqMyNat____x40_NNG_MyNat_Definition___hyg_15_(x_1, x_2);
+lean_dec(x_2);
+lean_dec(x_1);
+x_4 = lean_box(x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_instBEqMyNat___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_alloc_closure((void*)(l___private_NNG_MyNat_Definition_0__beqMyNat____x40_NNG_MyNat_Definition___hyg_15____boxed), 2, 0);
+return x_1;
+}
+}
+static lean_object* _init_l_instBEqMyNat() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_instBEqMyNat___closed__1;
+return x_1;
+}
+}
+LEAN_EXPORT uint8_t l___private_NNG_MyNat_Definition_0__decEqMyNat____x40_NNG_MyNat_Definition___hyg_99_(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+if (lean_obj_tag(x_1) == 0)
+{
+if (lean_obj_tag(x_2) == 0)
+{
+uint8_t x_3; 
+x_3 = 1;
+return x_3;
+}
+else
+{
+uint8_t x_4; 
+x_4 = 0;
+return x_4;
+}
+}
+else
+{
+if (lean_obj_tag(x_2) == 0)
+{
+uint8_t x_5; 
+x_5 = 0;
+return x_5;
+}
+else
+{
+lean_object* x_6; lean_object* x_7; 
+x_6 = lean_ctor_get(x_1, 0);
+x_7 = lean_ctor_get(x_2, 0);
+x_1 = x_6;
+x_2 = x_7;
+goto _start;
+}
+}
+}
+}
+LEAN_EXPORT lean_object* l___private_NNG_MyNat_Definition_0__decEqMyNat____x40_NNG_MyNat_Definition___hyg_99____boxed(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+uint8_t x_3; lean_object* x_4; 
+x_3 = l___private_NNG_MyNat_Definition_0__decEqMyNat____x40_NNG_MyNat_Definition___hyg_99_(x_1, x_2);
+lean_dec(x_2);
+lean_dec(x_1);
+x_4 = lean_box(x_3);
+return x_4;
+}
+}
+LEAN_EXPORT uint8_t l_instDecidableEqMyNat(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+uint8_t x_3; 
+x_3 = l___private_NNG_MyNat_Definition_0__decEqMyNat____x40_NNG_MyNat_Definition___hyg_99_(x_1, x_2);
+return x_3;
+}
+}
+LEAN_EXPORT lean_object* l_instDecidableEqMyNat___boxed(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+uint8_t x_3; lean_object* x_4; 
+x_3 = l_instDecidableEqMyNat(x_1, x_2);
+lean_dec(x_2);
+lean_dec(x_1);
+x_4 = lean_box(x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_instInhabitedMyNat() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_box(0);
+return x_1;
+}
+}
+static lean_object* _init_l_term_u2115___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("termℕ", 7);
+return x_1;
+}
+}
+static lean_object* _init_l_term_u2115___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l_term_u2115___closed__1;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l_term_u2115___closed__3() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("ℕ", 3);
+return x_1;
+}
+}
+static lean_object* _init_l_term_u2115___closed__4() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_term_u2115___closed__3;
+x_2 = lean_alloc_ctor(5, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_term_u2115___closed__5() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; 
+x_1 = l_term_u2115___closed__2;
+x_2 = lean_unsigned_to_nat(1024u);
+x_3 = l_term_u2115___closed__4;
+x_4 = lean_alloc_ctor(3, 3, 0);
+lean_ctor_set(x_4, 0, x_1);
+lean_ctor_set(x_4, 1, x_2);
+lean_ctor_set(x_4, 2, x_3);
+return x_4;
+}
+}
+static lean_object* _init_l_term_u2115() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_term_u2115___closed__5;
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("MyNat", 5);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1;
+x_2 = l_String_toSubstring_x27(x_1);
+return x_2;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__4() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_2);
+lean_ctor_set(x_3, 1, x_1);
+return x_3;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__5() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3;
+x_2 = lean_alloc_ctor(0, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__6() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__5;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_2);
+lean_ctor_set(x_3, 1, x_1);
+return x_3;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__7() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__4;
+x_2 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__6;
+x_3 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_3, 0, x_1);
+lean_ctor_set(x_3, 1, x_2);
+return x_3;
+}
+}
+LEAN_EXPORT lean_object* l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1(lean_object* x_1, lean_object* x_2, lean_object* x_3) {
+_start:
+{
+lean_object* x_4; uint8_t x_5; 
+x_4 = l_term_u2115___closed__2;
+x_5 = l_Lean_Syntax_isOfKind(x_1, x_4);
+if (x_5 == 0)
+{
+lean_object* x_6; lean_object* x_7; 
+lean_dec(x_2);
+x_6 = lean_box(1);
+x_7 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_7, 0, x_6);
+lean_ctor_set(x_7, 1, x_3);
+return x_7;
+}
+else
+{
+lean_object* x_8; uint8_t x_9; lean_object* x_10; lean_object* x_11; lean_object* x_12; lean_object* x_13; lean_object* x_14; lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; 
+x_8 = lean_ctor_get(x_2, 5);
+lean_inc(x_8);
+x_9 = 0;
+x_10 = l_Lean_SourceInfo_fromRef(x_8, x_9);
+x_11 = lean_ctor_get(x_2, 2);
+lean_inc(x_11);
+x_12 = lean_ctor_get(x_2, 1);
+lean_inc(x_12);
+lean_dec(x_2);
+x_13 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3;
+x_14 = l_Lean_addMacroScope(x_12, x_13, x_11);
+x_15 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__2;
+x_16 = l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__7;
+x_17 = lean_alloc_ctor(3, 4, 0);
+lean_ctor_set(x_17, 0, x_10);
+lean_ctor_set(x_17, 1, x_15);
+lean_ctor_set(x_17, 2, x_14);
+lean_ctor_set(x_17, 3, x_16);
+x_18 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_18, 0, x_17);
+lean_ctor_set(x_18, 1, x_3);
+return x_18;
+}
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("ident", 5);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__1;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__3() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Lean", 4);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__4() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Parser", 6);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__5() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("Term", 4);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__6() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("app", 3);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__7() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; lean_object* x_4; lean_object* x_5; 
+x_1 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__3;
+x_2 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__4;
+x_3 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__5;
+x_4 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__6;
+x_5 = l_Lean_Name_mkStr4(x_1, x_2, x_3, x_4);
+return x_5;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__8() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_mk_string_from_bytes("null", 4);
+return x_1;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__9() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; lean_object* x_3; 
+x_1 = lean_box(0);
+x_2 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__8;
+x_3 = l_Lean_Name_str___override(x_1, x_2);
+return x_3;
+}
+}
+static lean_object* _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__10() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = lean_unsigned_to_nat(0u);
+x_2 = lean_mk_empty_array_with_capacity(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1(lean_object* x_1, lean_object* x_2, lean_object* x_3) {
+_start:
+{
+lean_object* x_4; uint8_t x_5; 
+x_4 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__2;
+lean_inc(x_1);
+x_5 = l_Lean_Syntax_isOfKind(x_1, x_4);
+if (x_5 == 0)
+{
+lean_object* x_6; uint8_t x_7; 
+x_6 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__7;
+lean_inc(x_1);
+x_7 = l_Lean_Syntax_isOfKind(x_1, x_6);
+if (x_7 == 0)
+{
+lean_object* x_8; lean_object* x_9; 
+lean_dec(x_1);
+x_8 = lean_box(0);
+x_9 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_9, 0, x_8);
+lean_ctor_set(x_9, 1, x_3);
+return x_9;
+}
+else
+{
+lean_object* x_10; lean_object* x_11; uint8_t x_12; 
+x_10 = lean_unsigned_to_nat(0u);
+x_11 = l_Lean_Syntax_getArg(x_1, x_10);
+lean_inc(x_11);
+x_12 = l_Lean_Syntax_isOfKind(x_11, x_4);
+if (x_12 == 0)
+{
+lean_object* x_13; lean_object* x_14; 
+lean_dec(x_11);
+lean_dec(x_1);
+x_13 = lean_box(0);
+x_14 = lean_alloc_ctor(1, 2, 0);
+lean_ctor_set(x_14, 0, x_13);
+lean_ctor_set(x_14, 1, x_3);
+return x_14;
+}
+else
+{
+lean_object* x_15; lean_object* x_16; lean_object* x_17; lean_object* x_18; uint8_t x_19; lean_object* x_20; lean_object* x_21; lean_object* x_22; lean_object* x_23; lean_object* x_24; lean_object* x_25; lean_object* x_26; lean_object* x_27; lean_object* x_28; lean_object* x_29; lean_object* x_30; 
+x_15 = lean_unsigned_to_nat(1u);
+x_16 = l_Lean_Syntax_getArg(x_1, x_15);
+lean_dec(x_1);
+x_17 = l_Lean_Syntax_getArgs(x_16);
+lean_dec(x_16);
+x_18 = l_Lean_replaceRef(x_11, x_2);
+lean_dec(x_11);
+x_19 = 0;
+x_20 = l_Lean_SourceInfo_fromRef(x_18, x_19);
+x_21 = l_term_u2115___closed__3;
+lean_inc(x_20);
+x_22 = lean_alloc_ctor(2, 2, 0);
+lean_ctor_set(x_22, 0, x_20);
+lean_ctor_set(x_22, 1, x_21);
+x_23 = l_term_u2115___closed__2;
+lean_inc(x_20);
+x_24 = l_Lean_Syntax_node1(x_20, x_23, x_22);
+x_25 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__10;
+x_26 = l_Array_append___rarg(x_25, x_17);
+x_27 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__9;
+lean_inc(x_20);
+x_28 = lean_alloc_ctor(1, 3, 0);
+lean_ctor_set(x_28, 0, x_20);
+lean_ctor_set(x_28, 1, x_27);
+lean_ctor_set(x_28, 2, x_26);
+x_29 = l_Lean_Syntax_node2(x_20, x_6, x_24, x_28);
+x_30 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_30, 0, x_29);
+lean_ctor_set(x_30, 1, x_3);
+return x_30;
+}
+}
+}
+else
+{
+lean_object* x_31; uint8_t x_32; lean_object* x_33; lean_object* x_34; lean_object* x_35; lean_object* x_36; lean_object* x_37; lean_object* x_38; 
+x_31 = l_Lean_replaceRef(x_1, x_2);
+lean_dec(x_1);
+x_32 = 0;
+x_33 = l_Lean_SourceInfo_fromRef(x_31, x_32);
+x_34 = l_term_u2115___closed__3;
+lean_inc(x_33);
+x_35 = lean_alloc_ctor(2, 2, 0);
+lean_ctor_set(x_35, 0, x_33);
+lean_ctor_set(x_35, 1, x_34);
+x_36 = l_term_u2115___closed__2;
+x_37 = l_Lean_Syntax_node1(x_33, x_36, x_35);
+x_38 = lean_alloc_ctor(0, 2, 0);
+lean_ctor_set(x_38, 0, x_37);
+lean_ctor_set(x_38, 1, x_3);
+return x_38;
+}
+}
+}
+LEAN_EXPORT lean_object* l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___boxed(lean_object* x_1, lean_object* x_2, lean_object* x_3) {
+_start:
+{
+lean_object* x_4; 
+x_4 = l___aux__NNG__MyNat__Definition______unexpand__MyNat__1(x_1, x_2, x_3);
+lean_dec(x_2);
+return x_4;
+}
+}
+static lean_object* _init_l_MyNat_instInhabitedMyNat() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_box(0);
+return x_1;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_myNatFromNat(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; uint8_t x_3; 
+x_2 = lean_unsigned_to_nat(0u);
+x_3 = lean_nat_dec_eq(x_1, x_2);
+if (x_3 == 0)
+{
+lean_object* x_4; lean_object* x_5; lean_object* x_6; lean_object* x_7; 
+x_4 = lean_unsigned_to_nat(1u);
+x_5 = lean_nat_sub(x_1, x_4);
+x_6 = l_MyNat_myNatFromNat(x_5);
+lean_dec(x_5);
+x_7 = lean_alloc_ctor(1, 1, 0);
+lean_ctor_set(x_7, 0, x_6);
+return x_7;
+}
+else
+{
+lean_object* x_8; 
+x_8 = lean_box(0);
+return x_8;
+}
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_myNatFromNat___boxed(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = l_MyNat_myNatFromNat(x_1);
+lean_dec(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_natFromMyNat(lean_object* x_1) {
+_start:
+{
+if (lean_obj_tag(x_1) == 0)
+{
+lean_object* x_2; 
+x_2 = lean_unsigned_to_nat(0u);
+return x_2;
+}
+else
+{
+lean_object* x_3; lean_object* x_4; lean_object* x_5; lean_object* x_6; 
+x_3 = lean_ctor_get(x_1, 0);
+x_4 = l_MyNat_natFromMyNat(x_3);
+x_5 = lean_unsigned_to_nat(1u);
+x_6 = lean_nat_add(x_4, x_5);
+lean_dec(x_4);
+return x_6;
+}
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_natFromMyNat___boxed(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = l_MyNat_natFromMyNat(x_1);
+lean_dec(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_ofNat(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = l_MyNat_myNatFromNat(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_ofNat___boxed(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = l_MyNat_ofNat(x_1);
+lean_dec(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_instToStringMyNat(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; lean_object* x_3; 
+x_2 = l_MyNat_natFromMyNat(x_1);
+x_3 = l_Nat_repr(x_2);
+return x_3;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_instToStringMyNat___boxed(lean_object* x_1) {
+_start:
+{
+lean_object* x_2; 
+x_2 = l_MyNat_instToStringMyNat(x_1);
+lean_dec(x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_one___closed__1() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = lean_unsigned_to_nat(0u);
+x_2 = l_MyNat_myNatFromNat(x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_one___closed__2() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = l_MyNat_one___closed__1;
+x_2 = lean_alloc_ctor(1, 1, 0);
+lean_ctor_set(x_2, 0, x_1);
+return x_2;
+}
+}
+static lean_object* _init_l_MyNat_one() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_MyNat_one___closed__2;
+return x_1;
+}
+}
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_MyNat_Definition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+l_instBEqMyNat___closed__1 = _init_l_instBEqMyNat___closed__1();
+lean_mark_persistent(l_instBEqMyNat___closed__1);
+l_instBEqMyNat = _init_l_instBEqMyNat();
+lean_mark_persistent(l_instBEqMyNat);
+l_instInhabitedMyNat = _init_l_instInhabitedMyNat();
+lean_mark_persistent(l_instInhabitedMyNat);
+l_term_u2115___closed__1 = _init_l_term_u2115___closed__1();
+lean_mark_persistent(l_term_u2115___closed__1);
+l_term_u2115___closed__2 = _init_l_term_u2115___closed__2();
+lean_mark_persistent(l_term_u2115___closed__2);
+l_term_u2115___closed__3 = _init_l_term_u2115___closed__3();
+lean_mark_persistent(l_term_u2115___closed__3);
+l_term_u2115___closed__4 = _init_l_term_u2115___closed__4();
+lean_mark_persistent(l_term_u2115___closed__4);
+l_term_u2115___closed__5 = _init_l_term_u2115___closed__5();
+lean_mark_persistent(l_term_u2115___closed__5);
+l_term_u2115 = _init_l_term_u2115();
+lean_mark_persistent(l_term_u2115);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__1);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__2 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__2();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__2);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__3);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__4 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__4();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__4);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__5 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__5();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__5);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__6 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__6();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__6);
+l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__7 = _init_l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__7();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______macroRules__term_u2115__1___closed__7);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__1 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__1();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__1);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__2 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__2();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__2);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__3 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__3();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__3);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__4 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__4();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__4);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__5 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__5();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__5);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__6 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__6();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__6);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__7 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__7();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__7);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__8 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__8();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__8);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__9 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__9();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__9);
+l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__10 = _init_l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__10();
+lean_mark_persistent(l___aux__NNG__MyNat__Definition______unexpand__MyNat__1___closed__10);
+l_MyNat_instInhabitedMyNat = _init_l_MyNat_instInhabitedMyNat();
+lean_mark_persistent(l_MyNat_instInhabitedMyNat);
+l_MyNat_one___closed__1 = _init_l_MyNat_one___closed__1();
+lean_mark_persistent(l_MyNat_one___closed__1);
+l_MyNat_one___closed__2 = _init_l_MyNat_one___closed__2();
+lean_mark_persistent(l_MyNat_one___closed__2);
+l_MyNat_one = _init_l_MyNat_one();
+lean_mark_persistent(l_MyNat_one);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/MyNat/Definition.c.trace b/server/nng/build/ir/NNG/MyNat/Definition.c.trace
new file mode 100644
index 0000000..78e3290
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Definition.c.trace
@@ -0,0 +1 @@
+6972496789146285202
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/MyNat/Multiplication.c b/server/nng/build/ir/NNG/MyNat/Multiplication.c
new file mode 100644
index 0000000..9da0f29
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Multiplication.c
@@ -0,0 +1,100 @@
+// Lean compiler output
+// Module: NNG.MyNat.Multiplication
+// Imports: Init NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+LEAN_EXPORT lean_object* l_MyNat_instMulMyNat;
+static lean_object* l_MyNat_instMulMyNat___closed__1;
+lean_object* l_MyNat_myNatFromNat(lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_mul___boxed(lean_object*, lean_object*);
+LEAN_EXPORT lean_object* l_MyNat_mul(lean_object*, lean_object*);
+lean_object* l_MyNat_add(lean_object*, lean_object*);
+static lean_object* l_MyNat_mul___closed__1;
+static lean_object* _init_l_MyNat_mul___closed__1() {
+_start:
+{
+lean_object* x_1; lean_object* x_2; 
+x_1 = lean_unsigned_to_nat(0u);
+x_2 = l_MyNat_myNatFromNat(x_1);
+return x_2;
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_mul(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+if (lean_obj_tag(x_2) == 0)
+{
+lean_object* x_3; 
+x_3 = l_MyNat_mul___closed__1;
+return x_3;
+}
+else
+{
+lean_object* x_4; lean_object* x_5; lean_object* x_6; 
+x_4 = lean_ctor_get(x_2, 0);
+x_5 = l_MyNat_mul(x_1, x_4);
+x_6 = l_MyNat_add(x_1, x_5);
+return x_6;
+}
+}
+}
+LEAN_EXPORT lean_object* l_MyNat_mul___boxed(lean_object* x_1, lean_object* x_2) {
+_start:
+{
+lean_object* x_3; 
+x_3 = l_MyNat_mul(x_1, x_2);
+lean_dec(x_2);
+lean_dec(x_1);
+return x_3;
+}
+}
+static lean_object* _init_l_MyNat_instMulMyNat___closed__1() {
+_start:
+{
+lean_object* x_1; 
+x_1 = lean_alloc_closure((void*)(l_MyNat_mul___boxed), 2, 0);
+return x_1;
+}
+}
+static lean_object* _init_l_MyNat_instMulMyNat() {
+_start:
+{
+lean_object* x_1; 
+x_1 = l_MyNat_instMulMyNat___closed__1;
+return x_1;
+}
+}
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_MyNat_Multiplication(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+l_MyNat_mul___closed__1 = _init_l_MyNat_mul___closed__1();
+lean_mark_persistent(l_MyNat_mul___closed__1);
+l_MyNat_instMulMyNat___closed__1 = _init_l_MyNat_instMulMyNat___closed__1();
+lean_mark_persistent(l_MyNat_instMulMyNat___closed__1);
+l_MyNat_instMulMyNat = _init_l_MyNat_instMulMyNat();
+lean_mark_persistent(l_MyNat_instMulMyNat);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/MyNat/Multiplication.c.trace b/server/nng/build/ir/NNG/MyNat/Multiplication.c.trace
new file mode 100644
index 0000000..a9ec026
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Multiplication.c.trace
@@ -0,0 +1 @@
+2052634667963101258
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/MyNat/Theorems/Addition.c b/server/nng/build/ir/NNG/MyNat/Theorems/Addition.c
new file mode 100644
index 0000000..a33cb00
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Theorems/Addition.c
@@ -0,0 +1,37 @@
+// Lean compiler output
+// Module: NNG.MyNat.Theorems.Addition
+// Imports: Init NNG.Metadata NNG.MyNat.Addition
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_Metadata(uint8_t builtin, lean_object*);
+lean_object* initialize_NNG_MyNat_Addition(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_MyNat_Theorems_Addition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_Metadata(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+res = initialize_NNG_MyNat_Addition(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/MyNat/Theorems/Addition.c.trace b/server/nng/build/ir/NNG/MyNat/Theorems/Addition.c.trace
new file mode 100644
index 0000000..bfa62e3
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Theorems/Addition.c.trace
@@ -0,0 +1 @@
+3227530040224467366
\ No newline at end of file
diff --git a/server/nng/build/ir/NNG/MyNat/Theorems/Proposition.c b/server/nng/build/ir/NNG/MyNat/Theorems/Proposition.c
new file mode 100644
index 0000000..4175d5f
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Theorems/Proposition.c
@@ -0,0 +1,29 @@
+// Lean compiler output
+// Module: NNG.MyNat.Theorems.Proposition
+// Imports: Init
+#include <lean/lean.h>
+#if defined(__clang__)
+#pragma clang diagnostic ignored "-Wunused-parameter"
+#pragma clang diagnostic ignored "-Wunused-label"
+#elif defined(__GNUC__) && !defined(__CLANG__)
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#pragma GCC diagnostic ignored "-Wunused-label"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#endif
+#ifdef __cplusplus
+extern "C" {
+#endif
+lean_object* initialize_Init(uint8_t builtin, lean_object*);
+static bool _G_initialized = false;
+LEAN_EXPORT lean_object* initialize_NNG_MyNat_Theorems_Proposition(uint8_t builtin, lean_object* w) {
+lean_object * res;
+if (_G_initialized) return lean_io_result_mk_ok(lean_box(0));
+_G_initialized = true;
+res = initialize_Init(builtin, lean_io_mk_world());
+if (lean_io_result_is_error(res)) return res;
+lean_dec_ref(res);
+return lean_io_result_mk_ok(lean_box(0));
+}
+#ifdef __cplusplus
+}
+#endif
diff --git a/server/nng/build/ir/NNG/MyNat/Theorems/Proposition.c.trace b/server/nng/build/ir/NNG/MyNat/Theorems/Proposition.c.trace
new file mode 100644
index 0000000..3b33097
--- /dev/null
+++ b/server/nng/build/ir/NNG/MyNat/Theorems/Proposition.c.trace
@@ -0,0 +1 @@
+483796173031302994
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG.ilean b/server/nng/build/lib/NNG.ilean
new file mode 100644
index 0000000..03c7188
--- /dev/null
+++ b/server/nng/build/lib/NNG.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG.olean b/server/nng/build/lib/NNG.olean
new file mode 100644
index 0000000..1712c51
Binary files /dev/null and b/server/nng/build/lib/NNG.olean differ
diff --git a/server/nng/build/lib/NNG.trace b/server/nng/build/lib/NNG.trace
new file mode 100644
index 0000000..813ce6e
--- /dev/null
+++ b/server/nng/build/lib/NNG.trace
@@ -0,0 +1 @@
+7356427851528760174
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Doc/Definitions.ilean b/server/nng/build/lib/NNG/Doc/Definitions.ilean
new file mode 100644
index 0000000..7158bdc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Doc/Definitions.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Doc.Definitions"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Doc/Definitions.olean b/server/nng/build/lib/NNG/Doc/Definitions.olean
new file mode 100644
index 0000000..5cb4d98
Binary files /dev/null and b/server/nng/build/lib/NNG/Doc/Definitions.olean differ
diff --git a/server/nng/build/lib/NNG/Doc/Definitions.trace b/server/nng/build/lib/NNG/Doc/Definitions.trace
new file mode 100644
index 0000000..a4001fc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Doc/Definitions.trace
@@ -0,0 +1 @@
+2922655963706979749
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Doc/Lemmas.ilean b/server/nng/build/lib/NNG/Doc/Lemmas.ilean
new file mode 100644
index 0000000..128363e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Doc/Lemmas.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Doc.Lemmas"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Doc/Lemmas.olean b/server/nng/build/lib/NNG/Doc/Lemmas.olean
new file mode 100644
index 0000000..f3f354e
Binary files /dev/null and b/server/nng/build/lib/NNG/Doc/Lemmas.olean differ
diff --git a/server/nng/build/lib/NNG/Doc/Lemmas.trace b/server/nng/build/lib/NNG/Doc/Lemmas.trace
new file mode 100644
index 0000000..a348b20
--- /dev/null
+++ b/server/nng/build/lib/NNG/Doc/Lemmas.trace
@@ -0,0 +1 @@
+16771103639053061509
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Doc/Tactics.ilean b/server/nng/build/lib/NNG/Doc/Tactics.ilean
new file mode 100644
index 0000000..4722546
--- /dev/null
+++ b/server/nng/build/lib/NNG/Doc/Tactics.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Doc.Tactics"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Doc/Tactics.olean b/server/nng/build/lib/NNG/Doc/Tactics.olean
new file mode 100644
index 0000000..abbc514
Binary files /dev/null and b/server/nng/build/lib/NNG/Doc/Tactics.olean differ
diff --git a/server/nng/build/lib/NNG/Doc/Tactics.trace b/server/nng/build/lib/NNG/Doc/Tactics.trace
new file mode 100644
index 0000000..5a55535
--- /dev/null
+++ b/server/nng/build/lib/NNG/Doc/Tactics.trace
@@ -0,0 +1 @@
+5348243054589539109
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition.ilean b/server/nng/build/lib/NNG/Levels/Addition.ilean
new file mode 100644
index 0000000..bc487b8
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Addition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition.olean b/server/nng/build/lib/NNG/Levels/Addition.olean
new file mode 100644
index 0000000..fa6e4be
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition.trace b/server/nng/build/lib/NNG/Levels/Addition.trace
new file mode 100644
index 0000000..97256e5
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition.trace
@@ -0,0 +1 @@
+2084978910118405033
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Addition/Level_1.ilean
new file mode 100644
index 0000000..bb66cc8
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.add_zero":{"usages":[[52,8,52,16]],"definition":null},"c:MyNat.add_succ":{"usages":[[57,8,57,16]],"definition":null},"c:MyNat":{"usages":[[40,9,40,10]],"definition":null},"c:Lean.Meta.tactic.hygienic":{"usages":[[10,11,10,26]],"definition":null}},"module":"NNG.Levels.Addition.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_1.olean b/server/nng/build/lib/NNG/Levels/Addition/Level_1.olean
new file mode 100644
index 0000000..05e0a5d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_1.trace b/server/nng/build/lib/NNG/Levels/Addition/Level_1.trace
new file mode 100644
index 0000000..09a9b3a
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_1.trace
@@ -0,0 +1 @@
+5269099431713252405
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Addition/Level_2.ilean
new file mode 100644
index 0000000..a4bb3ce
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.add_zero":{"usages":[[14,8,14,16],[52,6,52,14],[55,6,55,14]],"definition":null},"c:MyNat.add_succ":{"usages":[[16,8,16,16],[58,6,58,14],[59,6,59,14],[60,6,60,14]],"definition":null},"c:MyNat":{"usages":[[12,22,12,23],[36,13,36,14]],"definition":null},"c:AdditionWorld.zero_add":{"usages":[[45,8,45,16],[45,18,45,26]],"definition":[12,8,12,16]}},"module":"NNG.Levels.Addition.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_2.olean b/server/nng/build/lib/NNG/Levels/Addition/Level_2.olean
new file mode 100644
index 0000000..ea7bd68
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_2.trace b/server/nng/build/lib/NNG/Levels/Addition/Level_2.trace
new file mode 100644
index 0000000..14654bc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_2.trace
@@ -0,0 +1 @@
+17690234639472501785
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Addition/Level_3.ilean
new file mode 100644
index 0000000..0af6240
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.succ":{"usages":[[47,16,47,20],[47,29,47,33]],"definition":null},"c:MyNat.add_zero":{"usages":[[15,8,15,16],[16,8,16,16],[54,8,54,16],[55,8,55,16]],"definition":null},"c:MyNat.add_succ":{"usages":[[18,8,18,16],[19,8,19,16],[20,8,20,16],[57,8,57,16],[59,8,59,16]],"definition":null},"c:MyNat":{"usages":[[13,27,13,28],[47,11,47,12]],"definition":null},"c:AdditionWorld.add_assoc":{"usages":[],"definition":[13,8,13,17]}},"module":"NNG.Levels.Addition.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_3.olean b/server/nng/build/lib/NNG/Levels/Addition/Level_3.olean
new file mode 100644
index 0000000..29c607a
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_3.trace b/server/nng/build/lib/NNG/Levels/Addition/Level_3.trace
new file mode 100644
index 0000000..7d2c4df
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_3.trace
@@ -0,0 +1 @@
+18302928042269315295
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Addition/Level_4.ilean
new file mode 100644
index 0000000..c3a591a
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.succ":{"usages":[[13,29,13,33],[13,42,13,46]],"definition":null},"c:MyNat.add_zero":{"usages":[[15,8,15,16],[16,8,16,16],[39,10,39,18],[47,8,47,16]],"definition":null},"c:MyNat.add_succ":{"usages":[[18,8,18,16],[20,8,20,16],[43,10,43,18],[49,8,49,16]],"definition":null},"c:MyNat":{"usages":[[13,24,13,25],[35,11,35,12]],"definition":null},"c:AdditionWorld.zero_add":{"usages":[[38,10,38,18],[46,8,46,16]],"definition":null},"c:AdditionWorld.succ_add":{"usages":[[41,10,41,18],[51,8,51,16]],"definition":[13,8,13,16]}},"module":"NNG.Levels.Addition.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_4.olean b/server/nng/build/lib/NNG/Levels/Addition/Level_4.olean
new file mode 100644
index 0000000..5d36bd4
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_4.trace b/server/nng/build/lib/NNG/Levels/Addition/Level_4.trace
new file mode 100644
index 0000000..72e6acf
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_4.trace
@@ -0,0 +1 @@
+12154535057277385306
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_5.ilean b/server/nng/build/lib/NNG/Levels/Addition/Level_5.ilean
new file mode 100644
index 0000000..dea7a56
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.succ":{"usages":[[23,37,23,41],[45,14,45,18]],"definition":null},"c:MyNat.add_zero":{"usages":[[16,8,16,16],[48,6,48,14]],"definition":null},"c:MyNat.add_succ":{"usages":[[18,8,18,16],[47,6,47,14]],"definition":null},"c:MyNat":{"usages":[[13,24,13,25],[23,32,23,33],[45,9,45,10]],"definition":null},"c:AdditionWorld.zero_add":{"usages":[[15,8,15,16]],"definition":null},"c:AdditionWorld.succ_add":{"usages":[[20,8,20,16]],"definition":null},"c:AdditionWorld.one_eq_succ_zero":{"usages":[[46,6,46,22]],"definition":[23,8,23,24]},"c:AdditionWorld.add_comm":{"usages":[],"definition":[13,8,13,16]}},"module":"NNG.Levels.Addition.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_5.olean b/server/nng/build/lib/NNG/Levels/Addition/Level_5.olean
new file mode 100644
index 0000000..8c8847d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_5.trace b/server/nng/build/lib/NNG/Levels/Addition/Level_5.trace
new file mode 100644
index 0000000..b660c1d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_5.trace
@@ -0,0 +1 @@
+9679823460697032654
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_6.ilean b/server/nng/build/lib/NNG/Levels/Addition/Level_6.ilean
new file mode 100644
index 0000000..d1d3fc5
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat":{"usages":[[40,13,40,14]],"definition":null},"c:AdditionWorld.add_comm":{"usages":[[42,6,42,14]],"definition":null},"c:AdditionWorld.add_assoc":{"usages":[[41,6,41,15],[43,7,43,16]],"definition":null}},"module":"NNG.Levels.Addition.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_6.olean b/server/nng/build/lib/NNG/Levels/Addition/Level_6.olean
new file mode 100644
index 0000000..d015a75
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Addition/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Addition/Level_6.trace b/server/nng/build/lib/NNG/Levels/Addition/Level_6.trace
new file mode 100644
index 0000000..13460c6
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Addition/Level_6.trace
@@ -0,0 +1 @@
+17709657049698654137
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition.ilean
new file mode 100644
index 0000000..0b6e7cd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvAddition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition.olean b/server/nng/build/lib/NNG/Levels/AdvAddition.olean
new file mode 100644
index 0000000..ac8c8d7
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition.trace b/server/nng/build/lib/NNG/Levels/AdvAddition.trace
new file mode 100644
index 0000000..9116234
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition.trace
@@ -0,0 +1 @@
+7852774950450280612
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.ilean
new file mode 100644
index 0000000..e9fa163
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:not_false_iff":{"usages":[[17,75,17,88]],"definition":null},"c:ne_eq":{"usages":[[17,68,17,73]],"definition":null},"c:imp_self":{"usages":[[15,88,15,96]],"definition":null},"c:MyNat.zero_ne_succ":{"usages":[],"definition":[17,8,17,26]},"c:MyNat.zero":{"usages":[[17,37,17,41]],"definition":null},"c:MyNat.succ_inj":{"usages":[[22,10,22,18]],"definition":[15,8,15,22]},"c:MyNat.succ.injEq":{"usages":[[15,76,15,86]],"definition":null},"c:MyNat.succ":{"usages":[[15,35,15,39],[15,44,15,48],[17,44,17,48],[21,20,21,24],[21,29,21,33]],"definition":null},"c:MyNat":{"usages":[[15,30,15,31],[17,32,17,33],[21,11,21,12]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.olean
new file mode 100644
index 0000000..d9d3960
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.trace
new file mode 100644
index 0000000..d0094f7
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_1.trace
@@ -0,0 +1 @@
+9336372057508599589
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.ilean
new file mode 100644
index 0000000..2423540
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_10"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.olean
new file mode 100644
index 0000000..8352980
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.trace
new file mode 100644
index 0000000..ed3ffc8
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_10.trace
@@ -0,0 +1 @@
+4008453200266032081
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.ilean
new file mode 100644
index 0000000..6759c40
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_11"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.olean
new file mode 100644
index 0000000..502eea0
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.trace
new file mode 100644
index 0000000..5b253cc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_11.trace
@@ -0,0 +1 @@
+10015610238961501552
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.ilean
new file mode 100644
index 0000000..b770a6c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_12"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.olean
new file mode 100644
index 0000000..ae2e8a3
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.trace
new file mode 100644
index 0000000..15d3040
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_12.trace
@@ -0,0 +1 @@
+5389173862524826914
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.ilean
new file mode 100644
index 0000000..cd9ce1e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_13"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.olean
new file mode 100644
index 0000000..3204313
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.trace
new file mode 100644
index 0000000..3535774
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_13.trace
@@ -0,0 +1 @@
+185528048873600791
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.ilean
new file mode 100644
index 0000000..138951c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.olean
new file mode 100644
index 0000000..faa18fe
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.trace
new file mode 100644
index 0000000..dfa5b14
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_2.trace
@@ -0,0 +1 @@
+3507750203879559481
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.ilean
new file mode 100644
index 0000000..3e7a817
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.olean
new file mode 100644
index 0000000..6b13a3a
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.trace
new file mode 100644
index 0000000..410d78c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_3.trace
@@ -0,0 +1 @@
+18314890376638277065
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.ilean
new file mode 100644
index 0000000..e2bbb14
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.olean
new file mode 100644
index 0000000..48d1e85
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.trace
new file mode 100644
index 0000000..16e6312
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_4.trace
@@ -0,0 +1 @@
+2092365143561121648
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.ilean
new file mode 100644
index 0000000..3ab7757
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.olean
new file mode 100644
index 0000000..7df7752
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.trace
new file mode 100644
index 0000000..ff557f6
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_5.trace
@@ -0,0 +1 @@
+17123810049702200014
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.ilean
new file mode 100644
index 0000000..083387d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.olean
new file mode 100644
index 0000000..76fa3ba
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.trace
new file mode 100644
index 0000000..b56da14
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_6.trace
@@ -0,0 +1 @@
+9314509491732931710
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.ilean
new file mode 100644
index 0000000..8abd9ea
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.olean
new file mode 100644
index 0000000..c71b2ad
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.trace
new file mode 100644
index 0000000..2d90327
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_7.trace
@@ -0,0 +1 @@
+13172030794097753806
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.ilean
new file mode 100644
index 0000000..2b8dbbd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.olean
new file mode 100644
index 0000000..7130733
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.trace
new file mode 100644
index 0000000..c4f1af7
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_8.trace
@@ -0,0 +1 @@
+10314181165617171139
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.ilean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.ilean
new file mode 100644
index 0000000..19ae684
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvAddition.Level_9"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.olean b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.olean
new file mode 100644
index 0000000..4041be7
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.trace b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.trace
new file mode 100644
index 0000000..e3e3b96
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvAddition/Level_9.trace
@@ -0,0 +1 @@
+8205318715931175597
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication.ilean b/server/nng/build/lib/NNG/Levels/AdvMultiplication.ilean
new file mode 100644
index 0000000..34737bf
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvMultiplication"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication.olean b/server/nng/build/lib/NNG/Levels/AdvMultiplication.olean
new file mode 100644
index 0000000..28f757e
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvMultiplication.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication.trace b/server/nng/build/lib/NNG/Levels/AdvMultiplication.trace
new file mode 100644
index 0000000..c00fc7d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication.trace
@@ -0,0 +1 @@
+5627580921265871323
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.ilean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.ilean
new file mode 100644
index 0000000..91a3c8b
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvMultiplication.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.olean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.olean
new file mode 100644
index 0000000..73a306d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.trace b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.trace
new file mode 100644
index 0000000..fcd4fe6
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_1.trace
@@ -0,0 +1 @@
+5496292641504121726
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.ilean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.ilean
new file mode 100644
index 0000000..fc7bd0e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvMultiplication.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.olean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.olean
new file mode 100644
index 0000000..51c66e3
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.trace b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.trace
new file mode 100644
index 0000000..b982607
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_2.trace
@@ -0,0 +1 @@
+3065456568864785697
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.ilean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.ilean
new file mode 100644
index 0000000..da0b92f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvMultiplication.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.olean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.olean
new file mode 100644
index 0000000..ba6e67b
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.trace b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.trace
new file mode 100644
index 0000000..63f9ad3
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_3.trace
@@ -0,0 +1 @@
+11074674160667156308
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.ilean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.ilean
new file mode 100644
index 0000000..2e66b7c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.AdvMultiplication.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.olean b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.olean
new file mode 100644
index 0000000..6d38b1f
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.trace b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.trace
new file mode 100644
index 0000000..428ebc8
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvMultiplication/Level_4.trace
@@ -0,0 +1 @@
+5171635906789131558
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition.ilean
new file mode 100644
index 0000000..218a4e3
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition.olean b/server/nng/build/lib/NNG/Levels/AdvProposition.olean
new file mode 100644
index 0000000..16b6620
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition.trace b/server/nng/build/lib/NNG/Levels/AdvProposition.trace
new file mode 100644
index 0000000..4e9a102
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition.trace
@@ -0,0 +1 @@
+9478676650839776721
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.ilean
new file mode 100644
index 0000000..2d12035
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.olean
new file mode 100644
index 0000000..1b11931
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.trace
new file mode 100644
index 0000000..1fa48a1
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_1.trace
@@ -0,0 +1 @@
+13140666477521992594
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.ilean
new file mode 100644
index 0000000..16fdfad
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_10"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.olean
new file mode 100644
index 0000000..32789a4
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.trace
new file mode 100644
index 0000000..790c7bd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_10.trace
@@ -0,0 +1 @@
+18203712100298108367
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.ilean
new file mode 100644
index 0000000..4c29d19
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Lean.Meta.tactic.hygienic":{"usages":[[16,11,16,26]],"definition":null}},"module":"NNG.Levels.AdvProposition.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.olean
new file mode 100644
index 0000000..657c7f1
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.trace
new file mode 100644
index 0000000..f2787fb
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_2.trace
@@ -0,0 +1 @@
+10022829939796104452
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.ilean
new file mode 100644
index 0000000..1a8ae67
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.olean
new file mode 100644
index 0000000..8f33a29
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.trace
new file mode 100644
index 0000000..9e0f004
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_3.trace
@@ -0,0 +1 @@
+1967301918816512059
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.ilean
new file mode 100644
index 0000000..e3a22a9
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.olean
new file mode 100644
index 0000000..ce5a396
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.trace
new file mode 100644
index 0000000..c2fe35c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_4.trace
@@ -0,0 +1 @@
+16129653996493781623
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.ilean
new file mode 100644
index 0000000..d75a82f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Iff.mpr":{"usages":[[26,12,26,13],[27,12,27,13]],"definition":null},"c:Iff.mp":{"usages":[[22,12,22,13],[23,12,23,13]],"definition":null}},"module":"NNG.Levels.AdvProposition.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.olean
new file mode 100644
index 0000000..22b092d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.trace
new file mode 100644
index 0000000..30bf614
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_5.trace
@@ -0,0 +1 @@
+16436512257645906503
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.ilean
new file mode 100644
index 0000000..d905ba0
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.olean
new file mode 100644
index 0000000..44ef4c6
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.trace
new file mode 100644
index 0000000..bf05509
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_6.trace
@@ -0,0 +1 @@
+14208111587323885963
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.ilean
new file mode 100644
index 0000000..a96a651
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.olean
new file mode 100644
index 0000000..6ab7bd5
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.trace
new file mode 100644
index 0000000..807ca0c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_7.trace
@@ -0,0 +1 @@
+8730344058151551457
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.ilean
new file mode 100644
index 0000000..643b03f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.olean
new file mode 100644
index 0000000..4e1c038
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.trace
new file mode 100644
index 0000000..074308d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_8.trace
@@ -0,0 +1 @@
+14257091850430971994
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.ilean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.ilean
new file mode 100644
index 0000000..698cf65
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.AdvProposition.Level_9"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.olean b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.olean
new file mode 100644
index 0000000..59eba58
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.trace b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.trace
new file mode 100644
index 0000000..34aee37
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/AdvProposition/Level_9.trace
@@ -0,0 +1 @@
+14967413771991349992
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function.ilean b/server/nng/build/lib/NNG/Levels/Function.ilean
new file mode 100644
index 0000000..a133d3d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function.olean b/server/nng/build/lib/NNG/Levels/Function.olean
new file mode 100644
index 0000000..c10f466
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function.trace b/server/nng/build/lib/NNG/Levels/Function.trace
new file mode 100644
index 0000000..a011cea
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function.trace
@@ -0,0 +1 @@
+4955068752717367929
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_1.ilean
new file mode 100644
index 0000000..7fc2359
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_1.olean b/server/nng/build/lib/NNG/Levels/Function/Level_1.olean
new file mode 100644
index 0000000..217974c
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_1.trace b/server/nng/build/lib/NNG/Levels/Function/Level_1.trace
new file mode 100644
index 0000000..3648ee3
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_1.trace
@@ -0,0 +1 @@
+11635906400192042058
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_2.ilean
new file mode 100644
index 0000000..ec4a0b4
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat":{"usages":[[18,6,18,7],[18,10,18,11]],"definition":null}},"module":"NNG.Levels.Function.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_2.olean b/server/nng/build/lib/NNG/Levels/Function/Level_2.olean
new file mode 100644
index 0000000..b1d64b0
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_2.trace b/server/nng/build/lib/NNG/Levels/Function/Level_2.trace
new file mode 100644
index 0000000..2f74304
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_2.trace
@@ -0,0 +1 @@
+5739902419023245944
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_3.ilean
new file mode 100644
index 0000000..b66fa84
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_3.olean b/server/nng/build/lib/NNG/Levels/Function/Level_3.olean
new file mode 100644
index 0000000..e983b55
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_3.trace b/server/nng/build/lib/NNG/Levels/Function/Level_3.trace
new file mode 100644
index 0000000..3765006
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_3.trace
@@ -0,0 +1 @@
+13295869598671621401
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_4.ilean
new file mode 100644
index 0000000..77fbcf0
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_4.olean b/server/nng/build/lib/NNG/Levels/Function/Level_4.olean
new file mode 100644
index 0000000..15bb087
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_4.trace b/server/nng/build/lib/NNG/Levels/Function/Level_4.trace
new file mode 100644
index 0000000..f73245d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_4.trace
@@ -0,0 +1 @@
+2060723493075565450
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_5.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_5.ilean
new file mode 100644
index 0000000..d2a8ae7
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_5.olean b/server/nng/build/lib/NNG/Levels/Function/Level_5.olean
new file mode 100644
index 0000000..7650835
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_5.trace b/server/nng/build/lib/NNG/Levels/Function/Level_5.trace
new file mode 100644
index 0000000..348e271
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_5.trace
@@ -0,0 +1 @@
+33560334747064612
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_6.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_6.ilean
new file mode 100644
index 0000000..f7560be
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_6.olean b/server/nng/build/lib/NNG/Levels/Function/Level_6.olean
new file mode 100644
index 0000000..e5f7236
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_6.trace b/server/nng/build/lib/NNG/Levels/Function/Level_6.trace
new file mode 100644
index 0000000..4fcc927
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_6.trace
@@ -0,0 +1 @@
+11236535691868165392
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_7.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_7.ilean
new file mode 100644
index 0000000..90b502f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_7.olean b/server/nng/build/lib/NNG/Levels/Function/Level_7.olean
new file mode 100644
index 0000000..e6462ba
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_7.trace b/server/nng/build/lib/NNG/Levels/Function/Level_7.trace
new file mode 100644
index 0000000..81404ca
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_7.trace
@@ -0,0 +1 @@
+13833688845280623014
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_8.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_8.ilean
new file mode 100644
index 0000000..cd7e338
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Empty":{"usages":[[17,35,17,40],[17,49,17,54]],"definition":null}},"module":"NNG.Levels.Function.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_8.olean b/server/nng/build/lib/NNG/Levels/Function/Level_8.olean
new file mode 100644
index 0000000..c7c1107
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_8.trace b/server/nng/build/lib/NNG/Levels/Function/Level_8.trace
new file mode 100644
index 0000000..247b254
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_8.trace
@@ -0,0 +1 @@
+3072509448285891874
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_9.ilean b/server/nng/build/lib/NNG/Levels/Function/Level_9.ilean
new file mode 100644
index 0000000..d096b16
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_9.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Function.Level_9"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_9.olean b/server/nng/build/lib/NNG/Levels/Function/Level_9.olean
new file mode 100644
index 0000000..054b056
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Function/Level_9.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Function/Level_9.trace b/server/nng/build/lib/NNG/Levels/Function/Level_9.trace
new file mode 100644
index 0000000..a7ade54
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Function/Level_9.trace
@@ -0,0 +1 @@
+11794545348629460374
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality.ilean b/server/nng/build/lib/NNG/Levels/Inequality.ilean
new file mode 100644
index 0000000..7d57769
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Inequality"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality.olean b/server/nng/build/lib/NNG/Levels/Inequality.olean
new file mode 100644
index 0000000..704725d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality.trace b/server/nng/build/lib/NNG/Levels/Inequality.trace
new file mode 100644
index 0000000..55184cc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality.trace
@@ -0,0 +1 @@
+9336489098668184658
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_1.ilean
new file mode 100644
index 0000000..6733e24
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_1.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_1.olean
new file mode 100644
index 0000000..6badbc8
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_1.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_1.trace
new file mode 100644
index 0000000..b5ffa38
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_1.trace
@@ -0,0 +1 @@
+15715418939533793162
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_10.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_10.ilean
new file mode 100644
index 0000000..a65afd3
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_10.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_10"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_10.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_10.olean
new file mode 100644
index 0000000..aa538d8
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_10.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_10.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_10.trace
new file mode 100644
index 0000000..eb78d47
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_10.trace
@@ -0,0 +1 @@
+8366872987603129236
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_11.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_11.ilean
new file mode 100644
index 0000000..2c2b577
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_11.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_11"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_11.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_11.olean
new file mode 100644
index 0000000..8357122
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_11.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_11.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_11.trace
new file mode 100644
index 0000000..3e01f72
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_11.trace
@@ -0,0 +1 @@
+9104254495681588724
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_12.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_12.ilean
new file mode 100644
index 0000000..9dbe64f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_12.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_12"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_12.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_12.olean
new file mode 100644
index 0000000..6fd62b4
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_12.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_12.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_12.trace
new file mode 100644
index 0000000..5115864
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_12.trace
@@ -0,0 +1 @@
+14766865931000247685
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_13.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_13.ilean
new file mode 100644
index 0000000..1329add
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_13.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_13"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_13.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_13.olean
new file mode 100644
index 0000000..82cc6dc
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_13.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_13.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_13.trace
new file mode 100644
index 0000000..e9d270e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_13.trace
@@ -0,0 +1 @@
+7236720961247687624
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_14.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_14.ilean
new file mode 100644
index 0000000..cefc752
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_14.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_14"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_14.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_14.olean
new file mode 100644
index 0000000..d6f3626
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_14.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_14.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_14.trace
new file mode 100644
index 0000000..e65fa47
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_14.trace
@@ -0,0 +1 @@
+17080990698887132932
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_15.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_15.ilean
new file mode 100644
index 0000000..5788bbd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_15.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_15"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_15.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_15.olean
new file mode 100644
index 0000000..518eea1
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_15.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_15.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_15.trace
new file mode 100644
index 0000000..9a7cd4e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_15.trace
@@ -0,0 +1 @@
+15808132813580510808
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_16.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_16.ilean
new file mode 100644
index 0000000..8264748
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_16.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_16"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_16.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_16.olean
new file mode 100644
index 0000000..f43231b
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_16.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_16.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_16.trace
new file mode 100644
index 0000000..65a9805
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_16.trace
@@ -0,0 +1 @@
+7637579646193566177
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_17.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_17.ilean
new file mode 100644
index 0000000..be9c88d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_17.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_17"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_17.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_17.olean
new file mode 100644
index 0000000..16d71a7
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_17.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_17.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_17.trace
new file mode 100644
index 0000000..1983d9c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_17.trace
@@ -0,0 +1 @@
+14135338231934509378
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_2.ilean
new file mode 100644
index 0000000..1e875fe
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_2.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_2.olean
new file mode 100644
index 0000000..bacec49
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_2.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_2.trace
new file mode 100644
index 0000000..6ada09d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_2.trace
@@ -0,0 +1 @@
+10180719735176429031
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_3.ilean
new file mode 100644
index 0000000..688fd92
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_3.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_3.olean
new file mode 100644
index 0000000..79d9320
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_3.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_3.trace
new file mode 100644
index 0000000..3e40b0c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_3.trace
@@ -0,0 +1 @@
+10425666160152371884
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_4.ilean
new file mode 100644
index 0000000..d4a0bc6
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_4.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_4.olean
new file mode 100644
index 0000000..fe9725a
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_4.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_4.trace
new file mode 100644
index 0000000..8aeaca9
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_4.trace
@@ -0,0 +1 @@
+5262542741621948205
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_5.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_5.ilean
new file mode 100644
index 0000000..1962e78
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_5.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_5.olean
new file mode 100644
index 0000000..1c31a9a
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_5.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_5.trace
new file mode 100644
index 0000000..e6f0c73
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_5.trace
@@ -0,0 +1 @@
+10099871401285119100
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_6.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_6.ilean
new file mode 100644
index 0000000..858767a
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_6.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_6.olean
new file mode 100644
index 0000000..3b628f6
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_6.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_6.trace
new file mode 100644
index 0000000..02ff8cd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_6.trace
@@ -0,0 +1 @@
+18291074078086778850
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_7.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_7.ilean
new file mode 100644
index 0000000..1f9ea1c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_7.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_7.olean
new file mode 100644
index 0000000..500f5f8
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_7.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_7.trace
new file mode 100644
index 0000000..ea65ccd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_7.trace
@@ -0,0 +1 @@
+4948452312372643925
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_8.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_8.ilean
new file mode 100644
index 0000000..e8cb103
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_8.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_8.olean
new file mode 100644
index 0000000..65571b5
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_8.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_8.trace
new file mode 100644
index 0000000..4675054
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_8.trace
@@ -0,0 +1 @@
+8910944482383625099
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_9.ilean b/server/nng/build/lib/NNG/Levels/Inequality/Level_9.ilean
new file mode 100644
index 0000000..19f48cc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_9.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Inequality.Level_9"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_9.olean b/server/nng/build/lib/NNG/Levels/Inequality/Level_9.olean
new file mode 100644
index 0000000..8578e0f
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Inequality/Level_9.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Inequality/Level_9.trace b/server/nng/build/lib/NNG/Levels/Inequality/Level_9.trace
new file mode 100644
index 0000000..3ed8de7
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Inequality/Level_9.trace
@@ -0,0 +1 @@
+10084756629938233881
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication.ilean b/server/nng/build/lib/NNG/Levels/Multiplication.ilean
new file mode 100644
index 0000000..1d9f701
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Multiplication"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication.olean b/server/nng/build/lib/NNG/Levels/Multiplication.olean
new file mode 100644
index 0000000..f4be59d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication.trace b/server/nng/build/lib/NNG/Levels/Multiplication.trace
new file mode 100644
index 0000000..aa0fcb8
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication.trace
@@ -0,0 +1 @@
+15100919068659915784
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.ilean
new file mode 100644
index 0000000..8509594
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.olean
new file mode 100644
index 0000000..12d08c4
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.trace
new file mode 100644
index 0000000..3ceaf84
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_1.trace
@@ -0,0 +1 @@
+2681194911731925232
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.ilean
new file mode 100644
index 0000000..c47bad5
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.olean
new file mode 100644
index 0000000..fb5224b
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.trace
new file mode 100644
index 0000000..51a6198
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_2.trace
@@ -0,0 +1 @@
+10245843345607907477
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.ilean
new file mode 100644
index 0000000..787ddb4
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.olean
new file mode 100644
index 0000000..40da5f1
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.trace
new file mode 100644
index 0000000..35f0e4e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_3.trace
@@ -0,0 +1 @@
+8940547588455067611
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.ilean
new file mode 100644
index 0000000..902b66c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.olean
new file mode 100644
index 0000000..b141353
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.trace
new file mode 100644
index 0000000..a872f1f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_4.trace
@@ -0,0 +1 @@
+14993641720182264605
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.ilean
new file mode 100644
index 0000000..2051584
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.olean
new file mode 100644
index 0000000..3a06142
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.trace
new file mode 100644
index 0000000..8105ffd
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_5.trace
@@ -0,0 +1 @@
+18175551488241716216
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.ilean
new file mode 100644
index 0000000..f75a308
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.olean
new file mode 100644
index 0000000..a6ed629
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.trace
new file mode 100644
index 0000000..2a12214
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_6.trace
@@ -0,0 +1 @@
+14531862140867195758
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.ilean
new file mode 100644
index 0000000..357d170
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.olean
new file mode 100644
index 0000000..99fc155
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.trace
new file mode 100644
index 0000000..ffc70ae
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_7.trace
@@ -0,0 +1 @@
+15474257035701176495
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.ilean
new file mode 100644
index 0000000..a86942d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.olean
new file mode 100644
index 0000000..4e1b545
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.trace
new file mode 100644
index 0000000..5757f7c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_8.trace
@@ -0,0 +1 @@
+3648854208530401287
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.ilean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.ilean
new file mode 100644
index 0000000..954badf
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Multiplication.Level_9"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.olean b/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.olean
new file mode 100644
index 0000000..2c95e7b
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.trace b/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.trace
new file mode 100644
index 0000000..2b1f5bf
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Multiplication/Level_9.trace
@@ -0,0 +1 @@
+4975536308483488989
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power.ilean b/server/nng/build/lib/NNG/Levels/Power.ilean
new file mode 100644
index 0000000..91694c3
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Power"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power.olean b/server/nng/build/lib/NNG/Levels/Power.olean
new file mode 100644
index 0000000..4466be0
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power.trace b/server/nng/build/lib/NNG/Levels/Power.trace
new file mode 100644
index 0000000..30f497d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power.trace
@@ -0,0 +1 @@
+12255441869344750286
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_1.ilean
new file mode 100644
index 0000000..2650824
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_1.olean b/server/nng/build/lib/NNG/Levels/Power/Level_1.olean
new file mode 100644
index 0000000..d073b53
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_1.trace b/server/nng/build/lib/NNG/Levels/Power/Level_1.trace
new file mode 100644
index 0000000..1d06499
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_1.trace
@@ -0,0 +1 @@
+3557218418934706832
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_2.ilean
new file mode 100644
index 0000000..f40d21b
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_2.olean b/server/nng/build/lib/NNG/Levels/Power/Level_2.olean
new file mode 100644
index 0000000..134d957
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_2.trace b/server/nng/build/lib/NNG/Levels/Power/Level_2.trace
new file mode 100644
index 0000000..f8ba540
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_2.trace
@@ -0,0 +1 @@
+3161955687484215514
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_3.ilean
new file mode 100644
index 0000000..0f08359
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_3.olean b/server/nng/build/lib/NNG/Levels/Power/Level_3.olean
new file mode 100644
index 0000000..5e6b126
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_3.trace b/server/nng/build/lib/NNG/Levels/Power/Level_3.trace
new file mode 100644
index 0000000..e72a579
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_3.trace
@@ -0,0 +1 @@
+13739636179189224786
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_4.ilean
new file mode 100644
index 0000000..e15a998
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_4.olean b/server/nng/build/lib/NNG/Levels/Power/Level_4.olean
new file mode 100644
index 0000000..b949d5a
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_4.trace b/server/nng/build/lib/NNG/Levels/Power/Level_4.trace
new file mode 100644
index 0000000..9672833
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_4.trace
@@ -0,0 +1 @@
+2643256504804179665
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_5.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_5.ilean
new file mode 100644
index 0000000..58da64c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_5.olean b/server/nng/build/lib/NNG/Levels/Power/Level_5.olean
new file mode 100644
index 0000000..fc8d506
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_5.trace b/server/nng/build/lib/NNG/Levels/Power/Level_5.trace
new file mode 100644
index 0000000..b91249f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_5.trace
@@ -0,0 +1 @@
+14401556251889401930
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_6.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_6.ilean
new file mode 100644
index 0000000..7068f22
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_6.olean b/server/nng/build/lib/NNG/Levels/Power/Level_6.olean
new file mode 100644
index 0000000..7e1e06d
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_6.trace b/server/nng/build/lib/NNG/Levels/Power/Level_6.trace
new file mode 100644
index 0000000..83f1ba1
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_6.trace
@@ -0,0 +1 @@
+16899530818829903575
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_7.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_7.ilean
new file mode 100644
index 0000000..1fff0b5
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_7.olean b/server/nng/build/lib/NNG/Levels/Power/Level_7.olean
new file mode 100644
index 0000000..851bccd
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_7.trace b/server/nng/build/lib/NNG/Levels/Power/Level_7.trace
new file mode 100644
index 0000000..36ca048
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_7.trace
@@ -0,0 +1 @@
+8728766979918631633
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_8.ilean b/server/nng/build/lib/NNG/Levels/Power/Level_8.ilean
new file mode 100644
index 0000000..ed85ad4
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:Bool.true":{"usages":[[17,6,17,10]],"definition":null}},"module":"NNG.Levels.Power.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_8.olean b/server/nng/build/lib/NNG/Levels/Power/Level_8.olean
new file mode 100644
index 0000000..a71ecab
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Power/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Power/Level_8.trace b/server/nng/build/lib/NNG/Levels/Power/Level_8.trace
new file mode 100644
index 0000000..83efa59
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Power/Level_8.trace
@@ -0,0 +1 @@
+16000363894567288792
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition.ilean b/server/nng/build/lib/NNG/Levels/Proposition.ilean
new file mode 100644
index 0000000..8f9853c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition.olean b/server/nng/build/lib/NNG/Levels/Proposition.olean
new file mode 100644
index 0000000..44b16fc
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition.trace b/server/nng/build/lib/NNG/Levels/Proposition.trace
new file mode 100644
index 0000000..91cc1cc
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition.trace
@@ -0,0 +1 @@
+8034725322126254406
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_1.ilean
new file mode 100644
index 0000000..f64af94
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_1.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_1.olean
new file mode 100644
index 0000000..26fc6ba
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_1.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_1.trace
new file mode 100644
index 0000000..71d00c7
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_1.trace
@@ -0,0 +1 @@
+18179347340463669579
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_2.ilean
new file mode 100644
index 0000000..1585563
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_2.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_2.olean
new file mode 100644
index 0000000..8ceb1c0
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_2.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_2.trace
new file mode 100644
index 0000000..9622df1
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_2.trace
@@ -0,0 +1 @@
+13217430201083326791
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_3.ilean
new file mode 100644
index 0000000..dafe381
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_3.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_3.olean
new file mode 100644
index 0000000..8f92154
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_3.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_3.trace
new file mode 100644
index 0000000..32f55cb
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_3.trace
@@ -0,0 +1 @@
+5299063203734346172
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_4.ilean
new file mode 100644
index 0000000..cfdd964
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_4.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_4.olean
new file mode 100644
index 0000000..7a1ff56
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_4.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_4.trace
new file mode 100644
index 0000000..619fbad
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_4.trace
@@ -0,0 +1 @@
+7415905544244480042
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_5.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_5.ilean
new file mode 100644
index 0000000..37f90ac
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_5.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_5"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_5.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_5.olean
new file mode 100644
index 0000000..f55c1b6
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_5.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_5.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_5.trace
new file mode 100644
index 0000000..067710f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_5.trace
@@ -0,0 +1 @@
+10613228186954229021
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_6.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_6.ilean
new file mode 100644
index 0000000..4111256
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_6.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_6"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_6.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_6.olean
new file mode 100644
index 0000000..6b83bc4
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_6.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_6.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_6.trace
new file mode 100644
index 0000000..a0c149e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_6.trace
@@ -0,0 +1 @@
+7894357058058824740
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_7.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_7.ilean
new file mode 100644
index 0000000..b80426e
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_7.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_7"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_7.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_7.olean
new file mode 100644
index 0000000..3de6399
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_7.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_7.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_7.trace
new file mode 100644
index 0000000..f619780
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_7.trace
@@ -0,0 +1 @@
+16656846323211551510
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_8.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_8.ilean
new file mode 100644
index 0000000..ae70d0f
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_8.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:not_iff_imp_false":{"usages":[[20,6,20,23],[21,6,21,23]],"definition":null}},"module":"NNG.Levels.Proposition.Level_8"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_8.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_8.olean
new file mode 100644
index 0000000..67b2caa
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_8.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_8.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_8.trace
new file mode 100644
index 0000000..ba8e72d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_8.trace
@@ -0,0 +1 @@
+13601220282574937828
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_9.ilean b/server/nng/build/lib/NNG/Levels/Proposition/Level_9.ilean
new file mode 100644
index 0000000..f912ff4
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_9.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Proposition.Level_9"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_9.olean b/server/nng/build/lib/NNG/Levels/Proposition/Level_9.olean
new file mode 100644
index 0000000..f50411a
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Proposition/Level_9.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Proposition/Level_9.trace b/server/nng/build/lib/NNG/Levels/Proposition/Level_9.trace
new file mode 100644
index 0000000..4a5bc97
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Proposition/Level_9.trace
@@ -0,0 +1 @@
+15399361750882572321
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial.ilean b/server/nng/build/lib/NNG/Levels/Tutorial.ilean
new file mode 100644
index 0000000..ad2b129
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Levels.Tutorial"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial.olean b/server/nng/build/lib/NNG/Levels/Tutorial.olean
new file mode 100644
index 0000000..d8fae45
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Tutorial.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial.trace b/server/nng/build/lib/NNG/Levels/Tutorial.trace
new file mode 100644
index 0000000..f666963
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial.trace
@@ -0,0 +1 @@
+1595615440839641244
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.ilean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.ilean
new file mode 100644
index 0000000..7eb784c
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat":{"usages":[[26,13,26,14]],"definition":null}},"module":"NNG.Levels.Tutorial.Level_1"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.olean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.olean
new file mode 100644
index 0000000..d4067b6
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.trace b/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.trace
new file mode 100644
index 0000000..029fdab
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_1.trace
@@ -0,0 +1 @@
+17057151196775041350
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.ilean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.ilean
new file mode 100644
index 0000000..1f2e7eb
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat":{"usages":[[24,11,24,12]],"definition":null}},"module":"NNG.Levels.Tutorial.Level_2"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.olean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.olean
new file mode 100644
index 0000000..713786b
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.trace b/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.trace
new file mode 100644
index 0000000..f0c7b10
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_2.trace
@@ -0,0 +1 @@
+2087975388406110178
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.ilean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.ilean
new file mode 100644
index 0000000..7a02609
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.succ":{"usages":[[47,20,47,24],[47,35,47,39],[47,41,47,45],[47,51,47,55]],"definition":null},"c:MyNat":{"usages":[[47,11,47,12]],"definition":null}},"module":"NNG.Levels.Tutorial.Level_3"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.olean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.olean
new file mode 100644
index 0000000..1d7fadb
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.trace b/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.trace
new file mode 100644
index 0000000..4568320
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_3.trace
@@ -0,0 +1 @@
+2143617200443064964
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.ilean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.ilean
new file mode 100644
index 0000000..cb2073d
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.succ":{"usages":[[45,18,45,22],[45,27,45,31]],"definition":null},"c:MyNat.add_zero":{"usages":[[52,11,52,19]],"definition":null},"c:MyNat.add_succ":{"usages":[[49,11,49,19]],"definition":null},"c:MyNat":{"usages":[[45,9,45,10]],"definition":null}},"module":"NNG.Levels.Tutorial.Level_4"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.olean b/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.olean
new file mode 100644
index 0000000..a179d63
Binary files /dev/null and b/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.olean differ
diff --git a/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.trace b/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.trace
new file mode 100644
index 0000000..03fc4ca
--- /dev/null
+++ b/server/nng/build/lib/NNG/Levels/Tutorial/Level_4.trace
@@ -0,0 +1 @@
+7407492338022565581
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Metadata.ilean b/server/nng/build/lib/NNG/Metadata.ilean
new file mode 100644
index 0000000..36ba107
--- /dev/null
+++ b/server/nng/build/lib/NNG/Metadata.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{},"module":"NNG.Metadata"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Metadata.olean b/server/nng/build/lib/NNG/Metadata.olean
new file mode 100644
index 0000000..cf8ed32
Binary files /dev/null and b/server/nng/build/lib/NNG/Metadata.olean differ
diff --git a/server/nng/build/lib/NNG/Metadata.trace b/server/nng/build/lib/NNG/Metadata.trace
new file mode 100644
index 0000000..0a81af6
--- /dev/null
+++ b/server/nng/build/lib/NNG/Metadata.trace
@@ -0,0 +1 @@
+10126315224814379241
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Modifications/Tactics.ilean b/server/nng/build/lib/NNG/Modifications/Tactics.ilean
new file mode 100644
index 0000000..68608ba
--- /dev/null
+++ b/server/nng/build/lib/NNG/Modifications/Tactics.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:liftM":{"usages":[[65,12,65,17]],"definition":null},"c:_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.getElimNameInfo":{"usages":[[71,13,71,28]],"definition":null},"c:_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.generalizeVars":{"usages":[[71,47,71,61]],"definition":null},"c:_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.generalizeTargets":{"usages":[[71,29,71,46]],"definition":null},"c:_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.getAltNumFields":{"usages":[[52,13,52,28],[59,20,59,35]],"definition":null},"c:Unit.unit":{"usages":[[63,61,63,63]],"definition":null},"c:Pure.pure":{"usages":[[63,56,63,60],[69,2,69,6],[124,64,124,68]],"definition":null},"c:Option.some":{"usages":[[63,8,63,12]],"definition":null},"c:MyNat.zero":{"usages":[[42,4,42,8]],"definition":null},"c:MyNat.succ":{"usages":[[40,40,40,44],[43,4,43,8]],"definition":null},"c:MyNat.rfl":{"usages":[[123,9,123,18]],"definition":[121,16,121,19]},"c:MyNat.rewriteSeq":{"usages":[[21,9,21,25]],"definition":[19,16,19,26]},"c:MyNat.rec'":{"usages":[],"definition":[39,4,39,8]},"c:MyNat.induction":{"usages":[],"definition":[80,14,80,36]},"c:MyNat.evalRfl":{"usages":[],"definition":[123,24,123,31]},"c:MyNat.evalRewriteSeq":{"usages":[],"definition":[21,31,21,45]},"c:MyNat":{"usages":[[39,14,39,15],[40,17,40,18],[40,54,40,55]],"definition":null},"c:List.splitAtD":{"usages":[[60,39,60,47]],"definition":null},"c:List.map":{"usages":[[62,55,62,58]],"definition":null},"c:List":{"usages":[[56,18,56,22]],"definition":null},"c:Lean.withRef":{"usages":[[94,19,94,26]],"definition":null},"c:Lean.binderIdent":{"usages":[[81,30,81,41]],"definition":null},"c:Lean.Unhygienic.run":{"usages":[[60,59,60,73]],"definition":null},"c:Lean.TSyntax.raw":{"usages":[[83,38,83,39]],"definition":null},"c:Lean.Syntax.getSepArgs":{"usages":[[83,40,83,50]],"definition":null},"c:Lean.Syntax.getArgs":{"usages":[[56,44,56,51]],"definition":null},"c:Lean.Syntax":{"usages":[[53,82,53,88],[56,23,56,29]],"definition":null},"c:Lean.RBTree.toArray":{"usages":[[93,51,93,58]],"definition":null},"c:Lean.Parser.checkColGt":{"usages":[[81,24,81,29]],"definition":null},"c:Lean.Parser.Tactic.rwRuleSeq":{"usages":[[19,43,19,52]],"definition":null},"c:Lean.Parser.Tactic.location":{"usages":[[19,54,19,62]],"definition":null},"c:Lean.Parser.Tactic.config":{"usages":[[19,34,19,40]],"definition":null},"c:Lean.Parser.Tactic.casesTarget":{"usages":[[80,57,80,68]],"definition":null},"c:Lean.Parser.Tactic.ElimApp.evalNames":{"usages":[[98,21,98,38]],"definition":[53,4,53,21]},"c:Lean.Parser.Category.tactic":{"usages":[[19,67,19,73],[82,6,82,12],[121,29,121,35]],"definition":null},"c:Lean.Meta.withReducible":{"usages":[[124,34,124,47]],"definition":null},"c:Lean.Meta.throwTacticEx":{"usages":[[28,7,28,20]],"definition":null},"c:Lean.Meta.sortFVarIds":{"usages":[[93,37,93,48]],"definition":null},"c:Lean.Meta.mkGeneralizationForbiddenSet":{"usages":[[91,22,91,50]],"definition":null},"c:Lean.Meta.getFVarSetToGeneralize":{"usages":[[92,18,92,40]],"definition":null},"c:Lean.Meta.getElimInfo":{"usages":[[86,19,86,30]],"definition":null},"c:Lean.Meta.addImplicitTargets":{"usages":[[87,18,87,36]],"definition":null},"c:Lean.Meta.FVarSubst.apply":{"usages":[[67,30,67,35]],"definition":null},"c:Lean.Meta.ElimInfo.motivePos":{"usages":[[96,47,96,56]],"definition":null},"c:Lean.Meta.ElimInfo":{"usages":[[53,34,53,42]],"definition":null},"c:Lean.Meta.Cases.unifyEqs?":{"usages":[[63,26,63,41]],"definition":null},"c:Lean.MVarId.withContext":{"usages":[[67,8,67,19],[85,4,85,15],[90,6,90,17]],"definition":null},"c:Lean.MVarId.tryClear":{"usages":[[65,38,65,46]],"definition":null},"c:Lean.MVarId.revert":{"usages":[[93,27,93,33]],"definition":null},"c:Lean.MVarId.refl":{"usages":[[124,58,124,62]],"definition":null},"c:Lean.MVarId.introNP":{"usages":[[64,19,64,26]],"definition":null},"c:Lean.MVarId.introN":{"usages":[[62,23,62,29]],"definition":null},"c:Lean.MVarId.getTag":{"usages":[[94,75,94,81]],"definition":null},"c:Lean.MVarId.assign":{"usages":[[97,8,97,14]],"definition":null},"c:Lean.MVarId":{"usages":[[55,21,55,27]],"definition":null},"c:Lean.FVarId":{"usages":[[54,57,54,63]],"definition":null},"c:Lean.Expr.mvarId!":{"usages":[[96,59,96,66]],"definition":null},"c:Lean.Expr.getAppArgs":{"usages":[[95,37,95,47]],"definition":null},"c:Lean.Expr.fvarId!":{"usages":[[89,40,89,47]],"definition":null},"c:Lean.Expr.fvar":{"usages":[[67,39,67,44]],"definition":null},"c:Lean.Expr.addLocalVarInfoForBinderIdent":{"usages":[[67,51,67,80]],"definition":null},"c:Lean.Elab.Term.TermElabM":{"usages":[[55,4,55,13]],"definition":null},"c:Lean.Elab.Tactic.withRWRulesSeq":{"usages":[[24,2,24,16]],"definition":null},"c:Lean.Elab.Tactic.withLocation":{"usages":[[25,4,25,16]],"definition":null},"c:Lean.Elab.Tactic.throwNoGoalsToBeSolved":{"usages":[[84,35,84,57]],"definition":null},"c:Lean.Elab.Tactic.setGoals":{"usages":[[100,6,100,14]],"definition":null},"c:Lean.Elab.Tactic.rewriteTarget":{"usages":[[27,7,27,20]],"definition":null},"c:Lean.Elab.Tactic.rewriteLocalDecl":{"usages":[[26,7,26,23]],"definition":null},"c:Lean.Elab.Tactic.liftMetaTactic":{"usages":[[124,2,124,16]],"definition":null},"c:Lean.Elab.Tactic.getUnsolvedGoals":{"usages":[[84,16,84,32]],"definition":null},"c:Lean.Elab.Tactic.getNameOfIdent'":{"usages":[[62,60,62,75]],"definition":null},"c:Lean.Elab.Tactic.expandOptLocation":{"usages":[[23,15,23,32]],"definition":null},"c:Lean.Elab.Tactic.evalInduction.checkTargets":{"usages":[[88,4,88,30]],"definition":null},"c:Lean.Elab.Tactic.evalInduction":{"usages":[[71,65,71,78]],"definition":null},"c:Lean.Elab.Tactic.evalCases":{"usages":[[52,32,52,41]],"definition":null},"c:Lean.Elab.Tactic.elabRewriteConfig":{"usages":[[22,12,22,29]],"definition":null},"c:Lean.Elab.Tactic.elabCasesTargets":{"usages":[[83,16,83,32]],"definition":null},"c:Lean.Elab.Tactic.Tactic":{"usages":[[21,48,21,54],[123,34,123,40]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.setMotiveArg":{"usages":[[96,6,96,26]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.mkElimApp":{"usages":[[94,35,94,52]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.evalAlts.go":{"usages":[[52,42,52,61]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.Result.others":{"usages":[[100,38,100,44]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.Result.elimApp":{"usages":[[95,29,95,36],[97,22,97,29]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.Result.alts":{"usages":[[98,55,98,59]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.Alt.name":{"usages":[[58,8,58,12]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.Alt.mvarId":{"usages":[[58,25,58,31]],"definition":null},"c:Lean.Elab.Tactic.ElimApp.Alt":{"usages":[[53,58,53,69]],"definition":null},"c:Array.toList":{"usages":[[56,55,56,61],[100,46,100,52]],"definition":null},"c:Array.size":{"usages":[[99,35,99,39]],"definition":null},"c:Array.push":{"usages":[[68,25,68,29]],"definition":null},"c:Array.map":{"usages":[[89,33,89,36]],"definition":null},"c:Array.foldlM":{"usages":[[65,28,65,34]],"definition":null},"c:Array":{"usages":[[53,52,53,57],[54,51,54,56],[55,15,55,20]],"definition":null}},"module":"NNG.Modifications.Tactics"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/Modifications/Tactics.olean b/server/nng/build/lib/NNG/Modifications/Tactics.olean
new file mode 100644
index 0000000..2ed7adb
Binary files /dev/null and b/server/nng/build/lib/NNG/Modifications/Tactics.olean differ
diff --git a/server/nng/build/lib/NNG/Modifications/Tactics.trace b/server/nng/build/lib/NNG/Modifications/Tactics.trace
new file mode 100644
index 0000000..b8a6417
--- /dev/null
+++ b/server/nng/build/lib/NNG/Modifications/Tactics.trace
@@ -0,0 +1 @@
+14754082556322596060
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Addition.ilean b/server/nng/build/lib/NNG/MyNat/Addition.ilean
new file mode 100644
index 0000000..871f7fa
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Addition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.zero":{"usages":[[7,7,7,8]],"definition":null},"c:MyNat.succ":{"usages":[[8,7,8,17],[8,23,8,33],[22,38,22,42],[22,48,22,52]],"definition":null},"c:MyNat.instAddMyNat":{"usages":[],"definition":[10,0,10,8]},"c:MyNat.add_zero":{"usages":[],"definition":[17,8,17,16]},"c:MyNat.add_succ":{"usages":[],"definition":[22,8,22,16]},"c:MyNat.add":{"usages":[[11,9,11,18]],"definition":[6,4,6,7]},"c:MyNat":{"usages":[[6,10,6,15],[6,18,6,23],[6,26,6,31],[10,15,10,20],[17,22,17,27],[22,24,22,29]],"definition":null},"c:Add.add":{"usages":[[11,2,11,5]],"definition":null},"c:Add":{"usages":[[10,11,10,14]],"definition":null}},"module":"NNG.MyNat.Addition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Addition.olean b/server/nng/build/lib/NNG/MyNat/Addition.olean
new file mode 100644
index 0000000..8bd7dc5
Binary files /dev/null and b/server/nng/build/lib/NNG/MyNat/Addition.olean differ
diff --git a/server/nng/build/lib/NNG/MyNat/Addition.trace b/server/nng/build/lib/NNG/MyNat/Addition.trace
new file mode 100644
index 0000000..9a68d6e
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Addition.trace
@@ -0,0 +1 @@
+2760095421866741095
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Definition.ilean b/server/nng/build/lib/NNG/MyNat/Definition.ilean
new file mode 100644
index 0000000..5cfc12f
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Definition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:rfl":{"usages":[[34,38,34,41]],"definition":null},"c:ToString.toString":{"usages":[[32,2,32,10],[32,16,32,24]],"definition":null},"c:ToString":{"usages":[[31,11,31,19]],"definition":null},"c:OfNat.ofNat":{"usages":[[29,2,29,7]],"definition":null},"c:OfNat":{"usages":[[28,27,28,32]],"definition":null},"c:Nat.zero":{"usages":[[20,4,20,12],[25,20,25,28]],"definition":null},"c:Nat.succ":{"usages":[[21,4,21,12],[26,20,26,28]],"definition":null},"c:Nat":{"usages":[[18,22,18,25],[23,31,23,34],[28,20,28,23]],"definition":null},"c:MyNat.zero_eq_0":{"usages":[],"definition":[34,8,34,17]},"c:MyNat.zero":{"usages":[[16,13,16,23],[20,18,20,28],[25,4,25,14],[34,20,34,30]],"definition":[5,2,5,6]},"c:MyNat.succ":{"usages":[[21,18,21,28],[26,4,26,14],[36,19,36,29]],"definition":[6,2,6,6]},"c:MyNat.one":{"usages":[],"definition":[36,4,36,7]},"c:MyNat.ofNat":{"usages":[],"definition":[28,9,28,14]},"c:MyNat.natFromMyNat":{"usages":[[32,26,32,38]],"definition":[23,4,23,16]},"c:MyNat.myNatFromNat":{"usages":[[29,11,29,23]],"definition":[18,4,18,16]},"c:MyNat.instToStringMyNat":{"usages":[],"definition":[31,0,31,8]},"c:MyNat.instInhabitedMyNat":{"usages":[],"definition":[15,0,15,8]},"c:MyNat":{"usages":[[10,16,10,21],[15,21,15,26],[18,29,18,34],[23,22,23,27],[28,33,28,38],[31,20,31,25],[36,10,36,15]],"definition":[4,10,4,15]},"c:Inhabited.default":{"usages":[[16,2,16,9]],"definition":null},"c:Inhabited":{"usages":[[7,27,7,36],[15,11,15,20]],"definition":null},"c:DecidableEq":{"usages":[[7,14,7,25]],"definition":null},"c:BEq":{"usages":[[7,9,7,12]],"definition":null}},"module":"NNG.MyNat.Definition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Definition.olean b/server/nng/build/lib/NNG/MyNat/Definition.olean
new file mode 100644
index 0000000..a7c648d
Binary files /dev/null and b/server/nng/build/lib/NNG/MyNat/Definition.olean differ
diff --git a/server/nng/build/lib/NNG/MyNat/Definition.trace b/server/nng/build/lib/NNG/MyNat/Definition.trace
new file mode 100644
index 0000000..78e3290
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Definition.trace
@@ -0,0 +1 @@
+6972496789146285202
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Multiplication.ilean b/server/nng/build/lib/NNG/MyNat/Multiplication.ilean
new file mode 100644
index 0000000..7338002
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Multiplication.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.zero":{"usages":[[7,7,7,8]],"definition":null},"c:MyNat.succ":{"usages":[[15,36,15,40]],"definition":null},"c:MyNat.mul_zero":{"usages":[],"definition":[13,6,13,14]},"c:MyNat.mul_succ":{"usages":[],"definition":[15,6,15,14]},"c:MyNat.mul":{"usages":[[11,9,11,18]],"definition":[6,4,6,7]},"c:MyNat.instMulMyNat":{"usages":[],"definition":[10,0,10,8]},"c:MyNat":{"usages":[[6,10,6,15],[6,18,6,23],[6,26,6,31],[10,15,10,20],[13,20,13,25],[15,22,15,27]],"definition":null},"c:Mul.mul":{"usages":[[11,2,11,5]],"definition":null},"c:Mul":{"usages":[[10,11,10,14]],"definition":null}},"module":"NNG.MyNat.Multiplication"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Multiplication.olean b/server/nng/build/lib/NNG/MyNat/Multiplication.olean
new file mode 100644
index 0000000..ff3bb8b
Binary files /dev/null and b/server/nng/build/lib/NNG/MyNat/Multiplication.olean differ
diff --git a/server/nng/build/lib/NNG/MyNat/Multiplication.trace b/server/nng/build/lib/NNG/MyNat/Multiplication.trace
new file mode 100644
index 0000000..a9ec026
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Multiplication.trace
@@ -0,0 +1 @@
+2052634667963101258
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Theorems/Addition.ilean b/server/nng/build/lib/NNG/MyNat/Theorems/Addition.ilean
new file mode 100644
index 0000000..b6b1277
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Theorems/Addition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:MyNat.zero_add":{"usages":[[36,8,36,16]],"definition":[5,8,5,22]},"c:MyNat.succ_add":{"usages":[[41,8,41,16]],"definition":[24,8,24,22]},"c:MyNat.succ":{"usages":[[24,35,24,39],[24,48,24,52],[44,43,44,47]],"definition":null},"c:MyNat.one_eq_succ_zero":{"usages":[],"definition":[44,8,44,30]},"c:MyNat.add_zero":{"usages":[[7,8,7,16],[15,8,15,16],[16,8,16,16],[26,8,26,16],[27,8,27,16],[37,8,37,16]],"definition":null},"c:MyNat.add_succ":{"usages":[[9,8,9,16],[18,8,18,16],[19,8,19,16],[20,8,20,16],[29,8,29,16],[31,8,31,16],[39,8,39,16]],"definition":null},"c:MyNat.add_comm":{"usages":[],"definition":[34,8,34,22]},"c:MyNat.add_assoc":{"usages":[],"definition":[13,8,13,23]},"c:MyNat":{"usages":[[5,28,5,29],[13,33,13,34],[24,30,24,31],[34,30,34,31],[44,38,44,39]],"definition":null}},"module":"NNG.MyNat.Theorems.Addition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Theorems/Addition.olean b/server/nng/build/lib/NNG/MyNat/Theorems/Addition.olean
new file mode 100644
index 0000000..d44df58
Binary files /dev/null and b/server/nng/build/lib/NNG/MyNat/Theorems/Addition.olean differ
diff --git a/server/nng/build/lib/NNG/MyNat/Theorems/Addition.trace b/server/nng/build/lib/NNG/MyNat/Theorems/Addition.trace
new file mode 100644
index 0000000..bfa62e3
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Theorems/Addition.trace
@@ -0,0 +1 @@
+3227530040224467366
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.ilean b/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.ilean
new file mode 100644
index 0000000..163a9b6
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.ilean
@@ -0,0 +1 @@
+{"version":1,"references":{"c:not_iff_imp_false":{"usages":[],"definition":[0,8,0,25]},"c:Bool.false":{"usages":[[0,49,0,54]],"definition":null}},"module":"NNG.MyNat.Theorems.Proposition"}
\ No newline at end of file
diff --git a/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.olean b/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.olean
new file mode 100644
index 0000000..c520fbe
Binary files /dev/null and b/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.olean differ
diff --git a/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.trace b/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.trace
new file mode 100644
index 0000000..3b33097
--- /dev/null
+++ b/server/nng/build/lib/NNG/MyNat/Theorems/Proposition.trace
@@ -0,0 +1 @@
+483796173031302994
\ No newline at end of file
diff --git a/server/nng/lake-manifest.json b/server/nng/lake-manifest.json
new file mode 100644
index 0000000..7534416
--- /dev/null
+++ b/server/nng/lake-manifest.json
@@ -0,0 +1,28 @@
+{"version": 4,
+ "packagesDir": "lake-packages",
+ "packages":
+ [{"git":
+   {"url": "https://github.com/leanprover-community/mathlib4.git",
+    "subDir?": null,
+    "rev": "fc4a489c2af75f687338fe85c8901335360f8541",
+    "name": "mathlib",
+    "inputRev?": "fc4a489c2af75f687338fe85c8901335360f8541"}},
+  {"git":
+   {"url": "https://github.com/gebner/quote4",
+    "subDir?": null,
+    "rev": "cc915afc9526e904a7b61f660d330170f9d60dd7",
+    "name": "Qq",
+    "inputRev?": "master"}},
+  {"git":
+   {"url": "https://github.com/JLimperg/aesop",
+    "subDir?": null,
+    "rev": "071464ac36e339afb7a87640aa1f8121f707a59a",
+    "name": "aesop",
+    "inputRev?": "master"}},
+  {"path": {"name": "GameServer", "dir": "./../leanserver"}},
+  {"git":
+   {"url": "https://github.com/leanprover/std4",
+    "subDir?": null,
+    "rev": "44a92d84c31a88b9af9329a441890ad449d8cd5f",
+    "name": "std",
+    "inputRev?": "main"}}]}
diff --git a/server/nng/lakefile.lean b/server/nng/lakefile.lean
new file mode 100644
index 0000000..942473c
--- /dev/null
+++ b/server/nng/lakefile.lean
@@ -0,0 +1,14 @@
+import Lake
+open Lake DSL
+
+require GameServer from ".."/"leanserver"
+
+
+require mathlib from git
+  "https://github.com/leanprover-community/mathlib4.git" @ "fc4a489c2af75f687338fe85c8901335360f8541"
+package NNG
+
+@[default_target]
+lean_lib NNG {
+  moreLeanArgs := #["-DautoImplicit=false"]
+}
diff --git a/server/nng/lean-toolchain b/server/nng/lean-toolchain
new file mode 100644
index 0000000..7f0fd43
--- /dev/null
+++ b/server/nng/lean-toolchain
@@ -0,0 +1 @@
+leanprover/lean4:nightly-2023-03-09
diff --git a/server/server.Dockerfile b/server/server.Dockerfile
index e056a94..7cf6aee 100644
--- a/server/server.Dockerfile
+++ b/server/server.Dockerfile
@@ -1,15 +1,15 @@
+ARG GAME_DIR
 FROM elan:latest
 
 WORKDIR /
 
 # Copy lean files
 COPY leanserver ./leanserver
-COPY testgame ./testgame
-# TODO: make `testgame` a build argument
+COPY $GAME_DIR ./$GAME_DIR
+# TODO: make `adam` a build argument
 
 WORKDIR /leanserver
 RUN rm -f ./build/bin/gameserver
 RUN lake build
 
 WORKDIR /leanserver/build/bin/
-CMD ["./gameserver", "--server"]
diff --git a/server/testgame/TestGame.lean b/server/testgame/TestGame.lean
deleted file mode 100644
index f48f3f7..0000000
--- a/server/testgame/TestGame.lean
+++ /dev/null
@@ -1,45 +0,0 @@
-import TestGame.Metadata
-
-import TestGame.Levels.Proposition
-import TestGame.Levels.Implication
-import TestGame.Levels.Predicate
-import TestGame.Levels.Contradiction
-import TestGame.Levels.Prime
-import TestGame.Levels.Sum
--- import TestGame.Levels.Induction
-
-import TestGame.Levels.Numbers
-import TestGame.Levels.Inequality
-
-import TestGame.Levels.LeanStuff
-import TestGame.Levels.SetTheory
-import TestGame.Levels.Function
-import TestGame.Levels.SetFunction
-import TestGame.Levels.LinearAlgebra
-
-
-
-Game "TestGame"
-Title "Lean 4 game"
-Introduction
-"
-TODO
-"
-
-Conclusion
-"Fertig!"
-
-
-Path Proposition → Implication → Predicate
-Path Predicate → Contradiction → Sum → LeanStuff
-Path LeanStuff → SetTheory → SetTheory2 → SetFunction
-
-Path Predicate → Prime -- → Induction
-Path Sum → Inequality -- → Induction
-Path Inequality → Function
-
-Path SetTheory2 → Numbers
-Path Module → Basis → Module2
-Path LeanStuff → Function → SetFunction
-
-MakeGame
diff --git a/server/testgame/TestGame/LemmaDocs.lean b/server/testgame/TestGame/LemmaDocs.lean
deleted file mode 100644
index 3898ba9..0000000
--- a/server/testgame/TestGame/LemmaDocs.lean
+++ /dev/null
@@ -1,206 +0,0 @@
-import GameServer.Commands
-
--- Wird im Level "Implication 11" ohne Beweis angenommen.
-LemmaDoc not_not as not_not in "Logic"
-"
-### Aussage
-
-`¬¬A ↔ A`
-
-### Annahmen
-
-`(A : Prop)`
-"
-
--- Wird im Level "Implication 10" ohne Beweis angenommen.
-LemmaDoc not_or_of_imp as not_or_of_imp in "Logic"
-"
-### Aussage
-
-`¬A ∨ B`
-
-### Annahmen
-
-`(A B : Prop)`\\
-`(h : A → B)`
-"
-
--- Wird im Level "Implication 12" bewiesen.
-LemmaDoc imp_iff_not_or as imp_iff_not_or in "Logic"
-"
-### Aussage
-
-`(A → B) ↔ ¬A ∨ B`
-
-### Annahmen
-
-`(A B : Prop)`
-"
-
-
-LemmaDoc Nat.succ_pos as Nat.succ_pos in "Nat"
-"
-"
-
-LemmaDoc Nat.pos_iff_ne_zero as Nat.pos_iff_ne_zero in "Nat"
-"
-"
-
-LemmaDoc zero_add as zero_add in "Addition"
-"This lemma says `∀ a : ℕ, 0 + a = a`."
-
-LemmaDoc add_zero as add_zero in "Addition"
-"This lemma says `∀ a : ℕ, a + 0 = a`."
-
-LemmaDoc add_succ as add_succ in "Addition"
-"This lemma says `∀ a b : ℕ, a + succ b = succ (a + b)`."
-
-LemmaDoc not_forall as not_forall in "Logic"
-"`∀ (A : Prop), ¬(∀ x, A) ↔ ∃x, (¬A)`."
-
-LemmaDoc not_exists as not_exists in "Logic"
-"`∀ (A : Prop), ¬(∃ x, A) ↔ ∀x, (¬A)`."
-
-DefinitionDoc Even
-"
-`even n` ist definiert als `∃ r, a = 2 * r`.
-Die Definition kann man mit `unfold even at *` einsetzen.
-"
-
-DefinitionDoc Odd
-"
-`odd n` ist definiert als `∃ r, a = 2 * r + 1`.
-Die Definition kann man mit `unfold odd at *` einsetzen.
-"
-
-DefinitionDoc Injective
-"
-`Injective f` ist definiert als
-
-```
-∀ a b, f a = f b → a = b
-```
-definiert.
-"
-
-DefinitionDoc Surjective
-"
-`Surjective f` ist definiert als
-
-```
-∀ a, (∃ b, f a = b)
-```
-"
-
-DefinitionDoc Bijective
-"
-"
-
-DefinitionDoc LeftInverse
-"
-"
-
-DefinitionDoc RightInverse
-"
-"
-
-DefinitionDoc StrictMono
-"
-`StrictMono f` ist definiert als
-
-```
-∀ a b, a < b → f a < f b
-```
-
-"
-
-LemmaDoc even_iff_not_odd as even_iff_not_odd in "Nat"
-"`Even n ↔ ¬ (Odd n)`"
-
-LemmaDoc odd_iff_not_even as odd_iff_not_even in "Nat"
-"`Odd n ↔ ¬ (Even n)`"
-
-LemmaDoc even_square as even_square in "Nat"
-"`∀ (n : ℕ), Even n → Even (n ^ 2)`"
-
-
-
-
-LemmaDoc mem_univ as mem_univ in "Set"
-"x ∈ @univ α"
-
-LemmaDoc not_mem_empty as not_mem_empty in "Set"
-""
-
-LemmaDoc empty_subset as empty_subset in "Set"
-""
-
-LemmaDoc Subset.antisymm_iff as Subset.antisymm_iff in "Set"
-""
-
-
-
-LemmaDoc Nat.prime_def_lt'' as Nat.prime_def_lt'' in "Nat"
-""
-
-
-LemmaDoc Finset.sum_add_distrib as Finset.sum_add_distrib in "Sum"
-""
-
-LemmaDoc Fin.sum_univ_castSucc as Fin.sum_univ_castSucc in "Sum"
-""
-
-LemmaDoc Nat.succ_eq_add_one as Nat.succ_eq_add_one in "Sum"
-""
-
-LemmaDoc add_comm as add_comm in "Nat"
-""
-
-LemmaDoc mul_add as mul_add in "Nat"
-""
-
-LemmaDoc add_mul as add_mul in "Nat"
-""
-
-LemmaDoc arithmetic_sum as arithmetic_sum in "Sum"
-""
-
-LemmaDoc add_pow_two as add_pow_two in "Nat"
-""
-
-LemmaDoc Finset.sum_comm as Finset.sum_comm in "Sum"
-""
-
-LemmaDoc Function.comp_apply as Function.comp_apply in "Function"
-""
-
-LemmaDoc not_le as not_le in "Logic"
-""
-
-LemmaDoc if_pos as if_pos in "Logic"
-""
-
-LemmaDoc if_neg as if_neg in "Logic"
-""
-
-LemmaDoc StrictMono.injective as StrictMono.injective in "Function"
-""
-
-LemmaDoc StrictMono.add as StrictMono.add in "Function"
-""
-
-LemmaDoc Odd.strictMono_pow as Odd.strictMono_pow in "Function"
-""
-
-LemmaDoc Exists.choose as Exists.choose in "Function"
-""
-
-LemmaDoc Exists.choose_spec as Exists.choose_spec in "Function"
-""
-LemmaDoc congrArg as congrArg in "Function"
-""
-LemmaDoc congrFun as congrFun in "Function"
-""
-
-LemmaDoc Iff.symm as Iff.symm in "Logic"
-""
diff --git a/server/testgame/TestGame/Levels/Contradiction.lean b/server/testgame/TestGame/Levels/Contradiction.lean
deleted file mode 100644
index 5805bb1..0000000
--- a/server/testgame/TestGame/Levels/Contradiction.lean
+++ /dev/null
@@ -1,16 +0,0 @@
-import TestGame.Levels.Contradiction.L01_Have
-import TestGame.Levels.Contradiction.L02_Suffices
-import TestGame.Levels.Contradiction.L03_ByContra
-import TestGame.Levels.Contradiction.L04_ByContra
-import TestGame.Levels.Contradiction.L05_Contrapose
-import TestGame.Levels.Contradiction.L06_Summary
-
-Game "TestGame"
-World "Contradiction"
-Title "Widerspruch"
-
-Introduction "
-Ihr begebt euch auf die Suche nach *Oddeus*. Nach etwas rumfragen, kommt ihr tatsächlich an
-eine Dornenfestung und nachdem ihr erklärt habt, wer ihr seit, werdet ihr auf eine Audienz
-gebeten.
-"
diff --git a/server/testgame/TestGame/Levels/Function.lean b/server/testgame/TestGame/Levels/Function.lean
deleted file mode 100644
index 0d2770d..0000000
--- a/server/testgame/TestGame/Levels/Function.lean
+++ /dev/null
@@ -1,24 +0,0 @@
-import TestGame.Levels.Function.L01_Function
-import TestGame.Levels.Function.L02_Let
-import TestGame.Levels.Function.L03_Piecewise
-import TestGame.Levels.Function.L04_Injective
-import TestGame.Levels.Function.L05_Injective
-import TestGame.Levels.Function.L06_Injective
-import TestGame.Levels.Function.L07_Surjective
-import TestGame.Levels.Function.L08_Bijective
-import TestGame.Levels.Function.L09_Inverse
-import TestGame.Levels.Function.L11_Inverse
-
-Game "TestGame"
-World "Function"
-Title "Abbildungen"
-
-Introduction "
-Auf der Suche nach dem Buch der Urbilder landet ihr auf einem kleinen Mond, der bis auf
-eine Insel komplett mit Wasser bedeckt zu sein scheint.
-
-Auf der Insel seht ihr verschiedene große und kleine Behausungen, manche aus Stroh und Holz,
-vereinzelte aus Lehm.
-
-Planlos geht ihr zum ersten Haus bei dem jemand vorne außen sitzt.
-"
diff --git a/server/testgame/TestGame/Levels/Induction.lean b/server/testgame/TestGame/Levels/Induction.lean
deleted file mode 100644
index c79daa1..0000000
--- a/server/testgame/TestGame/Levels/Induction.lean
+++ /dev/null
@@ -1,5 +0,0 @@
-import TestGame.Levels.Induction.L01_Induction
-
-Game "TestGame"
-World "Induction"
-Title "Übungen Induktions"
diff --git a/server/testgame/TestGame/Levels/Inequality.lean b/server/testgame/TestGame/Levels/Inequality.lean
deleted file mode 100644
index 12df4bf..0000000
--- a/server/testgame/TestGame/Levels/Inequality.lean
+++ /dev/null
@@ -1,8 +0,0 @@
-import TestGame.Levels.Inequality.L01_LE
-import TestGame.Levels.Inequality.L02_Pos
-import TestGame.Levels.Inequality.L03_Linarith
-import TestGame.Levels.Inequality.L04_Linarith
-
-Game "TestGame"
-World "Inequality"
-Title "Ungleichung"
diff --git a/server/testgame/TestGame/Levels/Inequality/L01_LE.lean b/server/testgame/TestGame/Levels/Inequality/L01_LE.lean
deleted file mode 100644
index e3d1b9c..0000000
--- a/server/testgame/TestGame/Levels/Inequality/L01_LE.lean
+++ /dev/null
@@ -1,24 +0,0 @@
-import TestGame.Metadata
-
-Game "TestGame"
-World "Inequality"
-Level 1
-
-Title "Kleinergleich"
-
-Introduction
-"
-Ungleichheiten werden in Lean generell immer als Kleinergleich `≤` (`\\le`) oder `<`
-geschrieben.
-
-Die Symbole `≥` und `>` gibt es zwar auch, sind aber nur Notation für die gleiche
-Aussage mit `≤` und `<`.
-
-Zudem sind `<` und `≤` auf `ℕ` so definiert, dass `0 < n` und `1 ≤ n` per Definition
-äquivalent sind. Die folgende Aussage ist also mit `rfl` beweisbar.
-"
-
-Statement
-"$0 < n$ und $1 ≤ n$ sind äquivalente Aussagen."
-    (n m : ℕ) : m < n ↔ m.succ ≤ n := by
-  rfl
diff --git a/server/testgame/TestGame/Levels/Inequality/L02_Pos.lean b/server/testgame/TestGame/Levels/Inequality/L02_Pos.lean
deleted file mode 100644
index 9ebd15c..0000000
--- a/server/testgame/TestGame/Levels/Inequality/L02_Pos.lean
+++ /dev/null
@@ -1,78 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Tactic.LibrarySearch
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "Inequality"
-Level 2
-
-Title "Kleinergleich"
-
-Introduction
-"
-Es gibt zwei intrinsische Möglichkeiten, zu sagen dass `(n : ℕ)` nicht Null ist:
-`n ≠ 0` oder `0 < n`.
-
-Das folgende Lemma kannst du immer brauchen um zwischen den beiden zu wechseln.
-
-(*Note:* `0 < n` wird in Lemma-Namen oft mit `_pos` beschrieben anstatt `zero_lt`, siehe z.B.
-`Nat.succ_pos`.)
-
-
-"
-
-Statement Nat.pos_iff_ne_zero
-"Benutze Induktion um zu zeigen, dass $0 < n$ und $n \\ne 0$ äquivalent sind."
-    (n : ℕ) : 0 < n ↔ n ≠ 0 := by
-  induction n
-  simp
-  constructor
-  intro
-  simp
-  intro
-  apply Nat.succ_pos
-
-NewTactic simp
-NewLemma Nat.succ_pos
-
-Hint : 0 < Nat.zero ↔ Nat.zero ≠ 0 =>
-"Den Induktionsanfang kannst du oft mit `simp` lösen."
-
-Hint (n : ℕ) (h : 0 < n ↔ n ≠ 0) : 0 < Nat.succ n ↔ Nat.succ n ≠ 0 =>
-"Jetzt der Induktionsschritt. Fang mal mit `constructor` an."
-
-HiddenHint (n : ℕ) : 0 < Nat.succ n → Nat.succ n ≠ 0 =>
-"Auch das kann `simp`."
-
-Hint (n : ℕ) : n.succ ≠ 0 =>
-"Auch das kann `simp`."
-
-Hint (n : ℕ) : 0 < Nat.succ n =>
-"Hier kannst du das Lemma `Nat.succ_pos` mit `apply` anwenden."
-
-
-
-/- Second, less ideal path -/
-
-Hint (n : ℕ) (h : 0 < n) : n ≠ 0 =>
-"An dieser Stelle fürst du am besten einen Beweis durch Widerspruch."
-
-HiddenHint (n : ℕ) (h : 0 < n) : n ≠ 0 =>
-"Das macht man mit `by_contra`."
-
-Hint (n : ℕ) (h : 0 < n) (g : n = 0) : False =>
-"Brauche `rw [_] at _` um eine Annahme `0 < 0` zu erzeugen."
-
-HiddenHint (h : 0 < 0) : False =>
-"Mit `contradiction` schliesst du den Widerspruchsbeweis."
-
-Hint (n : ℕ) (h : n ≠ 0) : 0 < n =>
-"Diese Richtung beweist du am besten per Induktion."
-
-HiddenHint (n : ℕ) (h : n ≠ 0) : 0 < n =>
-"Starte mit `induction n`."
-
- HiddenHint : 0 < Nat.zero =>
-"Mit `contradiction` kannst du den Induktionsanfang schliessen."
diff --git a/server/testgame/TestGame/Levels/Inequality/L03_Linarith.lean b/server/testgame/TestGame/Levels/Inequality/L03_Linarith.lean
deleted file mode 100644
index b63fab6..0000000
--- a/server/testgame/TestGame/Levels/Inequality/L03_Linarith.lean
+++ /dev/null
@@ -1,23 +0,0 @@
-import TestGame.Metadata
-import Mathlib.Tactic.Linarith
-
-Game "TestGame"
-World "Inequality"
-Level 3
-
-Title "Linarith"
-
-Introduction
-"
-Die Taktik `linarith` kann alle Systeme von linearen (Un-)gleichungen über `ℤ`, `ℚ`, etc. lösen.
-Über `ℕ` ist sie etwas schwächer, aber einfache Aussagen kann sie trotzdem beweisen.
-"
-
-Statement
-"Wenn $n \\ge 2$, zeige, dass $n$ nich Null sein kann."
-    (n : ℕ) (h : 2 ≤ n) : n ≠ 0 := by
-  linarith
-
-NewTactic linarith
-
-NewLemma Nat.pos_iff_ne_zero
diff --git a/server/testgame/TestGame/Levels/Inequality/L04_Linarith.lean b/server/testgame/TestGame/Levels/Inequality/L04_Linarith.lean
deleted file mode 100644
index b06c0fc..0000000
--- a/server/testgame/TestGame/Levels/Inequality/L04_Linarith.lean
+++ /dev/null
@@ -1,28 +0,0 @@
-import TestGame.Metadata
-import Mathlib.Tactic.Linarith
-
-Game "TestGame"
-World "Inequality"
-Level 4
-
-Title "Linarith"
-
-Introduction
-"
-Sobald man mit einem Ring arbeitet, der eine lineare Order hat (also z.B. `ℤ` oder `ℚ`),
-ist `linarith` stärker und kann Systeme von Gleichungen und Ungleichungen angehen.
-
-`linarith` kann aber nur mit linearen Ungleichungen umgehen, mit Termen der Form `x ^ 2`
-kann es nicht umgehen.
-"
-
-Statement
-"
-Angenommen man hat für zwei Ganzzahlen $x, y$ folgende Ungleichungen.
-$$
-\\begin{aligned} 5 * y &\\le 35 - 2 * x \\\\ 2 * y &\\le x + 3 \\end{aligned}
-$$
-Zeige, dass $y \\le 5$.
-"
-    (x y : ℤ) (h₂ : 5 * y ≤ 35 - 2 * x) (h₃ : 2 * y ≤ x + 3) : y ≤ 5 := by
-  linarith
diff --git a/server/testgame/TestGame/Levels/LeanStuff.lean b/server/testgame/TestGame/Levels/LeanStuff.lean
deleted file mode 100644
index c0e6935..0000000
--- a/server/testgame/TestGame/Levels/LeanStuff.lean
+++ /dev/null
@@ -1,8 +0,0 @@
-import TestGame.Levels.LeanStuff.L01_Type
-import TestGame.Levels.LeanStuff.L02_Universe
-import TestGame.Levels.LeanStuff.L03_ImplicitArguments
-import TestGame.Levels.LeanStuff.L04_InstanceArguments
-
-Game "TestGame"
-World "LeanStuff"
-Title "Lean"
diff --git a/server/testgame/TestGame/Levels/LeanStuff/L01_Type.lean b/server/testgame/TestGame/Levels/LeanStuff/L01_Type.lean
deleted file mode 100644
index 1a6fd1c..0000000
--- a/server/testgame/TestGame/Levels/LeanStuff/L01_Type.lean
+++ /dev/null
@@ -1,49 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "LeanStuff"
-Level 1
-
-Title "Typen"
-
-Introduction
-"
-Dieses Kapitel führt ein paar Lean-spezifische Sachen ein, die du wissen solltest.
-
-Mathematisch haben diese Sachen keinen Inhalt, aber es ist wichtig, dass du etwas
-verstehst wie Lean manche Sachen macht.
-
-Als erstes geht es um Typen.
-
-Oft sieht man Argumente von der Form `(U : Type)` was heisst \"sei $U$ ein Typ.\"
-Als Mathematiker kann man sich Typen ein bisschen wie Mengen vorstellen, in dem Sinn
-dass sie die Grundlage der Mathematik bilden: Alles sind Typen.
-
-Zum Beispiel ist `ℕ` der Typ der natürlichen Zahlen, `Prop` der Typ der logischen
-Aussagen, und ein Ring ist ein Typ `(R : Type)` zusammen mit einer Instanz `[Ring R]`,
-die sagt, dass auf diesem Typ eine Ringstruktur besteht.
-
-**Achtung**: Wie du aber gleich sehen wirst sind Typen und Mengen in Lean unterschiedliche
-Sachen.
-
-Hier ein kleines Beispiel zu Typen und Instanzen:
-"
-
-Statement
-""
-    (R : Type) [CommRing R] (a b : R) : a + b = b + a := by
-  ring
-
-Hint (R : Type) (h : CommRing R) (a : R) (b : R) : a + b = b + a =>
-"
-Die Taktik `ring` funktioniert in jedem Typen,
-ist aber stärker, je nach Instanz auf dem Typen.
-
-In Mathlib sind Instanzen `[CommSemiring ℕ]`, [CommRing ℤ]`, `[Field ℚ]`, etc. definiert.
-Die Taktik `ring` muss eine dieser Instanzen finden, die sagen, dass die Addition kommutative ist,
-damit das Lemma `add_comm` angewendet und die Aussage bewiesen werden kann.
-"
diff --git a/server/testgame/TestGame/Levels/LeanStuff/L02_Universe.lean b/server/testgame/TestGame/Levels/LeanStuff/L02_Universe.lean
deleted file mode 100644
index c75343e..0000000
--- a/server/testgame/TestGame/Levels/LeanStuff/L02_Universe.lean
+++ /dev/null
@@ -1,51 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "LeanStuff"
-Level 2
-
-Title "Universen"
-
-Introduction
-"
-Ein weitere Syntax, den man in Lean abundzu sieht sind Universen.
-
-Diese sind für Mathematiker erst einmal nicht so wichtig, und es reicht zu wissen,
-dass diese existieren.
-
-Da alle Objekte in Lean einen Typ haben, kann man sich fragen, welchen Typ hat eigentlich `Type`
-selber? Die Anwort darauf ist dass `Type` vom Typ `Type 1` ist und dieses wiederum vom Typ `Type 2`
-usw.
-
-Da Lemmas in Lean gerne so algemein wie möglich formuliert werden, sieht man oft `(R : Type _)`
-anstatt `(R : Type)`, wobei `_` einfach ein Platzhalter für eine Zahl ist.
-
-Alternativ kann man auch explizit Universum-Levels definieren, so sind die folgenden beiden
-Aussdrücke äquivalent:
-
-```
-variable (R : Type _)
-
-universe u
-variable (R : Type u)
-```
-
-In der Praxis kann man immer ohne bedenken `Type _` verwendenen und wenn man auf
-(mengentheoretische)
-Probleme stösst, muss man dan eventuell die Universen spezifizieren.
-
-*Die Normalform ist eigentlich `(R : Type _)` zu schreiben solange man kein Grund hat
-das Universum einzuschränken.*
-"
-
-Statement
-""
-    (R : Type _) [CommRing R] (a b : R) : a + b = b + a := by
-  ring
-
--- Hint (R : Type) (h : CommRing R) (a : R) (b : R) : a + b = b + a =>
--- ""
diff --git a/server/testgame/TestGame/Levels/LeanStuff/L03_ImplicitArguments.lean b/server/testgame/TestGame/Levels/LeanStuff/L03_ImplicitArguments.lean
deleted file mode 100644
index 1d85c83..0000000
--- a/server/testgame/TestGame/Levels/LeanStuff/L03_ImplicitArguments.lean
+++ /dev/null
@@ -1,63 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib
-import TestGame.Options.BigOperators
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "LeanStuff"
-Level 3
-
-Title "Implizite Argumente"
-
-Introduction
-"
-
-Auch wichtiger Syntax ist der Unterschied zwischen
-impliziten und expliziten Argumenten von Lemmas. **Explizite Argumente**
-schreibt man mit runden Klammern `()`, **impliziete Argumente** mit geschweiften `{}`.
-
-Als implizit werden alle Argumente markiert, die Lean selbständig aus dem Kontext
-erschliessen und einfüllen kann.
-
-Als Beispiel schauen wir uns ein bekanntes Lemma an:
-```
-lemma Fin.sum_univ_castSucc {β : Type _} [AddCommMonoid β] {n : ℕ} (f : Fin (n + 1) → β) :
-    ∑ i : Fin (n + 1), f i = ∑ i : Fin n, f (↑Fin.castSucc.toEmbedding i) + f (Fin.last n) := by
-  sorry
-```
-
-Hier ist unter anderem `n` als implizites Argument angegeben, da Lean aus `f` herauslesen kann,
-was `n` sein muss. Falls man trotzdem einmal das implizites Argument angeben muss
-(z.B. um `rw` zu helfen, wenn es mehrere Möglichkeiten gibt),
-kann man dies mit `Fin.sum_univ_castSucc (n := m + 1)` machen.
-"
-
-open BigOperators
-
-Statement
-"Zeige $(\\sum_{i=0}^{m} i) + (m + 1) = \\sum_{i=0}^{m + 1} i$."
-    (m : ℕ) :
-      ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i := by
-  rw [Fin.sum_univ_castSucc (n := m + 1)]
-  rfl
-
-OnlyTactic rw rfl
-
-NewLemma Fin.sum_univ_castSucc
-
-HiddenHint (m : ℕ) :
-  ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i =>
-"Das Lemma `Fin.sum_univ_castSucc` hilft."
-
-Hint (m : ℕ) :
-  ∑ i : Fin m, (Fin.castSucc.toEmbedding i : ℕ) + ↑(Fin.last m) + (m + 1) =
-  ∑ i : Fin (Nat.succ m + 1), ↑i =>
-"Hier hat `rw` die falsche der beiden Summen umgeschrieben. Hilf ihm mit
-`rw [Fin.sum_univ_castSucc (n := m + 1)]`."
-
-Hint (m : ℕ) :
-  ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) =
-  ∑ i : Fin (m + 1), ↑i + (m + 1) =>
-"Jetzt sind beide Seiten gleich und das Goal kann mit `rfl` geschlossen werden."
diff --git a/server/testgame/TestGame/Levels/LeanStuff/L04_InstanceArguments.lean b/server/testgame/TestGame/Levels/LeanStuff/L04_InstanceArguments.lean
deleted file mode 100644
index b06d3d2..0000000
--- a/server/testgame/TestGame/Levels/LeanStuff/L04_InstanceArguments.lean
+++ /dev/null
@@ -1,78 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib
-import TestGame.Options.BigOperators
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "LeanStuff"
-Level 4
-
-Title "Instanz-Argumente"
-
-Introduction
-"
-Bezüglich impliziten Argumente gibt es noch einige weitere Punkte oder Tricks,
-die man wissen sollte.
-
-* Instanz-Argumente wie `[Ring R]` sind auch impilzite Argumente. Der Unterschied ist, dass
-  Lean einen anderen Mechanismus braucht, um diese zu füllen: Es sucht nach einer entsprechenden
-  *Instanz* und, setzt die erste solche Instanz ein.
-  Ausserhalb eines Beweises könnte man auch mit
-  ```
-  #synth Ring ℤ
-  ```
-  testen, ob Lean eine ensprechende Instanz findet. Instanzen werden dafür gebraucht, Typen
-  mit (algebraischer) Stukturen zu versehen.
-* Ein `_` irgendwo im Lean-Code ist immer ein Platzhalter, den Lean versucht aus dem Kontext zu
-  füllen. Das kann praktisch sein, wenn man etwas nicht ausschreiben will, das offensichtlich ist.
-* Mit `@` kann man forcieren, dass alle Argumente explizit sind.
-  Für ein Lemma
-  ```
-  lemma not_or_of_imp {A B : Prop} (h : A → B) :
-      ¬A ∨ B := sorry
-  ```
-  heisst das zum Beispiel dass `not_or_of_imp g` das gleiche ist wie
-  `@not_or_of_imp _ _ g`.
-
-  Und `Fin.sum_univ_castSucc (n := m + 1)` könnte man auch als
-  `@Fin.sum_univ_castSucc _ _ (m + 1)` schreiben.
-"
-
-open BigOperators
-
-Statement
-"Zeige $(\\sum_{i=0}^{m} i) + (m + 1) = \\sum_{i=0}^{m + 1} i$."
-    (m : ℕ) :
-      ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i := by
-  rw [Fin.sum_univ_castSucc (n := m + 1)]
-  rfl
-
-OnlyTactic rw rfl
-
-NewLemma Fin.sum_univ_castSucc
-
-Hint (m : ℕ) :
-  ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i =>
-"
-  Probier nochmals das gleiche, diesmal mit
-```
-rw [@Fin.sum_univ_castSucc _ _ (m + 1)]
-```
-anstatt
-```
-rw [Fin.sum_univ_castSucc (n := m + 1)]
-```
-"
-
-Hint (m : ℕ) :
-  ∑ i : Fin m, (Fin.castSucc.toEmbedding i : ℕ) + ↑(Fin.last m) + (m + 1) =
-  ∑ i : Fin (Nat.succ m + 1), ↑i =>
-"Sackgasse!"
-
-
-Hint (m : ℕ) :
-  ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) =
-  ∑ i : Fin (m + 1), ↑i + (m + 1) =>
-"Jetzt sind beide Seiten gleich und das Goal kann mit `rfl` geschlossen werden."
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra.lean b/server/testgame/TestGame/Levels/LinearAlgebra.lean
deleted file mode 100644
index 816817f..0000000
--- a/server/testgame/TestGame/Levels/LinearAlgebra.lean
+++ /dev/null
@@ -1,35 +0,0 @@
-import TestGame.Levels.LinearAlgebra.L01_Module
-import TestGame.Levels.LinearAlgebra.L02_VectorNotation
-import TestGame.Levels.LinearAlgebra.L03_VectorNotation
-import TestGame.Levels.LinearAlgebra.L04_Submodule
-import TestGame.Levels.LinearAlgebra.L05_Submodule
-import TestGame.Levels.LinearAlgebra.L06_Span
-import TestGame.Levels.LinearAlgebra.L07_Span
-import TestGame.Levels.LinearAlgebra.L08_GeneratingSet
-
-import TestGame.Levels.LinearAlgebra.M01_LinearMap
-import TestGame.Levels.LinearAlgebra.M02_LinearIndep
-import TestGame.Levels.LinearAlgebra.M04_Basis
-import TestGame.Levels.LinearAlgebra.M05_Basis
-
-import TestGame.Levels.LinearAlgebra.N01_Span
-import TestGame.Levels.LinearAlgebra.N02_Span
-import TestGame.Levels.LinearAlgebra.N03_Idempotent
-import TestGame.Levels.LinearAlgebra.N04_Idempotent
-import TestGame.Levels.LinearAlgebra.N05_Sum
-import TestGame.Levels.LinearAlgebra.N06_Sum
-import TestGame.Levels.LinearAlgebra.N07_Prod
-import TestGame.Levels.LinearAlgebra.N08_Prod
-import TestGame.Levels.LinearAlgebra.N09_Prod
-
-Game "TestGame"
-World "Module"
-Title "Vektorraum"
-
-Game "TestGame"
-World "Basis"
-Title "Lineare Abbildungen"
-
-Game "TestGame"
-World "Module2"
-Title "Mehr Vektorräume"
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/L01_Module.lean b/server/testgame/TestGame/Levels/LinearAlgebra/L01_Module.lean
deleted file mode 100644
index b471da9..0000000
--- a/server/testgame/TestGame/Levels/LinearAlgebra/L01_Module.lean
+++ /dev/null
@@ -1,91 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Data.Real.Basic      -- definiert `ℝ`
-import Mathlib.Algebra.Module.Basic -- definiert `module`
-import Mathlib.Tactic.LibrarySearch
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "Module"
-Level 1
-
-Title "Module"
-
-Introduction
-"
-Vektorräume sind in Lean etwas algemeiner definiert, als dies normalerweise in
-einer Einführungsvorlesung antrifft: Man definiert ein \"Modul\" (Plural: Moduln)
-über einem Ring. Ein Modul über einem Körper wird auch \"Vektorraum\" genannt.
-Konkret heisst das:
-
-Sei `R` ein Ring. Ein `R`-Modul ist eine kommutative Gruppe `(V, +)` zusammen mit
-einer Abbildung `• : R × V → V` (Skalarmultiplitation genannt), die folgende
-Eigenschaften beliebige `(r s : R)` und `(v w : V)`erfüllt:
-- `r • (v + w) = r • v + r • w`
-- `(r + s) • v = r • v + s • v`
-- `(r * s) • v = r • s • v`
-- `1 • r = r`
-- `0 • v = 0`
-- `r • 0 = 0`
-
-Bemerkungen:
-1) Über einem `[field R]` sind die letzten beiden Eigenschaften überflüssig, diese kann
-   man beweisen, wenn man Cancellation (`a₁ + x = a₂ + x → a₁ = a₂`) hat. In einem generellen
-   Ring, muss das aber nicht gegeben sein (siehe Nullteiler).
-2) Die nötigen Annahmen um ein Modul in Lean zu erhalten sind tatsächlich noch etwas lockerer,
-   so muss `R` nicht ganz ein Ring sein (nur `[semiring R]`) und
-   `V` muss nicht ganz eine kommutative Gruppe sein (nur `[add_comm_monoid V]`).
-
-
-Einen abstrakten Vektorraum definiert man wie folgt:
-`variables {R V : Type*} [field R] [add_comm_monoid V] [module R V]`
-
-Wenn man hingegen konkret zeigen will, dass ein existierendes Objekt ein Vektorraum ist,
-kann man eine einsprechende Instanz wie folgt definieren:
-
-```
-instance Q_module : Module ℚ ℝ :=
-{ smul := λa r, ↑a * r
-  smul_zero := _
-  zero_smul := _
-  one_smul := _
-  smul_add := _
-  add_smul := _
-  mul_smul := _ }
-```
-Man muss also angeben, welche Skalarmultiplikation man gerne hätte
-(`smul`. In unserem Fall sagen wir einfach, diese soll Multiplikation in `ℝ` sein.)
-und dazu jegliche Beweise, dass die Skalarmultiplikation sich mit der Ringstruktur verträgt.
-Im nachfolgenden beweisen wir die Eigenschaften einzeln.
-"
-
-Statement
-"Zeige, dass $\\mathbb{R}$ ein $\\mathbb{Q}$-Modul ist."
-    : Module ℚ ℝ := by
-  refine {
-    smul := fun a r => ↑a * r
-    smul_zero := ?smul_zero
-    zero_smul := ?zero_smul
-    one_smul := ?one_smul
-    smul_add := ?smul_add
-    add_smul := ?add_smul
-    mul_smul := ?mul_smul }
-
-  · intro b
-    change (1 : ℚ) * b = b
-    rw [Rat.cast_one, one_mul]
-  · intro x y b
-    change (x * y : ℚ) * b = x * (y * b)
-    rw [Rat.cast_mul, mul_assoc]
-  · intro a
-    rw [smul_zero]
-  · intro a x y
-    change a * (x + y) = a * x + a * y
-    rw [mul_add]
-  · intro r s x
-    change (r + s : ℚ) * x = r * x + s * x
-    rw [Rat.cast_add, add_mul]
-  · intro a
-    change (0 : ℚ) * a = 0
-    simp
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/M02_LinearIndep.lean b/server/testgame/TestGame/Levels/LinearAlgebra/M02_LinearIndep.lean
deleted file mode 100644
index 0114b45..0000000
--- a/server/testgame/TestGame/Levels/LinearAlgebra/M02_LinearIndep.lean
+++ /dev/null
@@ -1,40 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Algebra.Module.Submodule.Lattice
-import Mathlib.Data.Real.Basic           -- definiert `ℝ`
-import Mathlib.Algebra.Module.LinearMap -- definiert `→ₗ`
-import Mathlib.Tactic.FinCases
-import Mathlib.Data.Fin.VecNotation
--- import Mathlib.LinearAlgebra.Finsupp
-import Mathlib.Algebra.BigOperators.Basic -- default
--- import Mathlib.LinearAlgebra.LinearIndependent
-
-Game "TestGame"
-World "Basis"
-Level 2
-
-Title "Lineare Unabhängigkeit"
-
---notation "ℝ²" => Fin 2 → ℝ
-
-Introduction
-"
-"
-
-Statement
-"Zeige, dass `![1, 0], ![1, 1]` linear unabhängig über `ℝ` sind."
-    : True := by -- linearIndependent ℝ ![(![1, 0] : ℝ²), ![1, 1]] := by
-  trivial
-
--- begin
---   rw fintype.linear_independent_iff,
---   intros c h,
---   simp at h,
---   intros i,
---   fin_cases i,
---   swap,
---   { exact h.2 },
---   { have h' := h.1,
---     rw [h.2, add_zero] at h',
---     exact h'}
--- end
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/M04_Basis.lean b/server/testgame/TestGame/Levels/LinearAlgebra/M04_Basis.lean
deleted file mode 100644
index 66c3304..0000000
--- a/server/testgame/TestGame/Levels/LinearAlgebra/M04_Basis.lean
+++ /dev/null
@@ -1,19 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Algebra.Module.Submodule.Lattice
-
-Game "TestGame"
-World "Basis"
-Level 4
-
-Title "Basis"
-
-Introduction
-"
-
-"
-
-Statement
-""
-    : True := by -- Basis (Fin 2) ℝ ℝ² := by
-  trivial
diff --git a/server/testgame/TestGame/Levels/LinearAlgebra/M05_Basis.lean b/server/testgame/TestGame/Levels/LinearAlgebra/M05_Basis.lean
deleted file mode 100644
index ed5be65..0000000
--- a/server/testgame/TestGame/Levels/LinearAlgebra/M05_Basis.lean
+++ /dev/null
@@ -1,19 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Algebra.Module.Submodule.Lattice
-
-Game "TestGame"
-World "Basis"
-Level 5
-
-Title "Lineare Abbildung"
-
-Introduction
-"
-
-"
-
-Statement
-""
-    : True := by
-  trivial
diff --git a/server/testgame/TestGame/Levels/Numbers.lean b/server/testgame/TestGame/Levels/Numbers.lean
deleted file mode 100644
index 622c5a4..0000000
--- a/server/testgame/TestGame/Levels/Numbers.lean
+++ /dev/null
@@ -1,2 +0,0 @@
-import TestGame.Levels.Numbers.L01_PNat
-import TestGame.Levels.Numbers.L02_PNat
diff --git a/server/testgame/TestGame/Levels/Prime.lean b/server/testgame/TestGame/Levels/Prime.lean
deleted file mode 100644
index c9fb5f6..0000000
--- a/server/testgame/TestGame/Levels/Prime.lean
+++ /dev/null
@@ -1,8 +0,0 @@
-import TestGame.Levels.Prime.L01_Dvd
-import TestGame.Levels.Prime.L04_Prime
-import TestGame.Levels.Prime.L05_Prime
-import TestGame.Levels.Prime.L06_ExistsUnique
-
-Game "TestGame"
-World "Prime"
-Title "Teilbarkeit"
diff --git a/server/testgame/TestGame/Levels/Prime/L01_Dvd.lean b/server/testgame/TestGame/Levels/Prime/L01_Dvd.lean
deleted file mode 100644
index 5edc0da..0000000
--- a/server/testgame/TestGame/Levels/Prime/L01_Dvd.lean
+++ /dev/null
@@ -1,52 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Tactic.Ring
-
-Game "TestGame"
-World "Prime"
-Level 1
-
-Title "Teilbarkeit"
-
-Introduction
-"
-Die Aussage \"$m$ teilt $n$.\" wird in Lean als `m | n` (`\\|`) geschrieben.
-
-**Wichtig:** `∣` (Teilbarkeit) ist ein spezielles Unicode Symbol, das nicht dem
-senkrechten Strich auf der Tastatur (`|`) entspricht. Man erhält es mit `\\|`.
-
-`m ∣ n` bedeutet `∃ c, n = m * c`, das heisst, man kann damit genau gleich umgehen
-wie mit einem `∃`-Quantifier.
-"
-
-Statement dvd_add
-  "Wenn $m$ ein Teiler von $n$ und $k$ ist, dann teilt es die Summe."
-  (n m k : ℕ) (h : m ∣ n) (g : m ∣ k) : m ∣ n + k := by
-  rcases h with ⟨x, h⟩
-  rcases g with ⟨y, g⟩
-  use x + y
-  rw [h, g]
-  ring
-
-HiddenHint (n : ℕ) (m : ℕ) (k : ℕ) (h : m ∣ n) (g : m ∣ k) : m ∣ n + k =>
-"
-Wenn man explizit mit der Definition von Teilbarkeit arbeiten will,
-sollte man als erstes alle Annahmen der Form `x ∣ y` mit `rcases` aufteilen.
-"
-
-HiddenHint (n : ℕ) (m : ℕ) (k : ℕ) (x : ℕ) (h : n = m * x) (g : m ∣ k) : m ∣ n + k =>
-"
-Wenn man explizit mit der Definition von Teilbarkeit arbeiten will,
-sollte man als erstes alle Annahmen der Form `x ∣ y` mit `rcases` aufteilen.
-"
-
-HiddenHint (n : ℕ) (m : ℕ) (k : ℕ) (y : ℕ)  (h : m ∣ n) (g : k = m * y) : m ∣ n + k =>
-"
-Wenn man explizit mit der Definition von Teilbarkeit arbeiten will,
-sollte man als erstes alle Annahmen der Form `x ∣ y` mit `rcases` aufteilen.
-"
-
-HiddenHint (n : ℕ) (m : ℕ) (k : ℕ) (x : ℕ) (y : ℕ) (h : n = m * x) (g : k = m * y) : m ∣ n + k =>
-"
-Jetzt kannst du mit `use` eine Zahl angeben, so dass $m * X = n + k$.
-"
diff --git a/server/testgame/TestGame/Levels/Prime/L04_Prime.lean b/server/testgame/TestGame/Levels/Prime/L04_Prime.lean
deleted file mode 100644
index 9256544..0000000
--- a/server/testgame/TestGame/Levels/Prime/L04_Prime.lean
+++ /dev/null
@@ -1,46 +0,0 @@
-import TestGame.Metadata
-import Mathlib.Data.Nat.Prime
-
-import Std.Tactic.RCases
-import Mathlib.Tactic.LeftRight
-import Mathlib.Tactic.Contrapose
-import Mathlib.Tactic.Use
-import Mathlib.Tactic.Ring
-
-import TestGame.ToBePorted
-
-Game "TestGame"
-World "Prime"
-Level 2
-
-Title "Primzahlen"
-
-Introduction
-"
-Eine Primzahl wird mit `(n : ℕ) (h : Nat.Prime n)` dargestellt.
-
-Wichtige Lemmas über Primzhalen werden mit
-
-```
-import Data.Nat.Prime
-```
-importiert (siehe
-[Docs](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime.html)).
-
-Insbesondere `Nat.prime_def_lt''` welches die aus der Schule bekannte Definition einer
-Primzahl `Prime p ↔ 2 ≤ p ∧ (∀ m, m ∣ p → m = 1 ∨ m = p)` gibt.
-
-Beachte: In Lean gibt es auch noch den Ausdruck `Prime n`, der beschreibt generelle
-Primelemente in einem generellen Ring. Wenn man mit natürlichen
-Zahlen arbeitet, ist es besser `Nat.Prime` zu verwenden, obwohl man natürlich zeigen kann
-dass die beiden äquivalent sind.
-"
-
-Statement
-"Zeige dass die einzigen Teiler einer Primzahl $1$ und $p$ sind."
-    (p : ℕ) (h : Nat.Prime p) : ∀ (x : ℕ), (x ∣ p) → x = 1 ∨ x = p := by
-  rw [Nat.prime_def_lt''] at h
-  rcases h with ⟨_, h₂⟩
-  assumption
-
-NewLemma Nat.prime_def_lt''
diff --git a/server/testgame/TestGame/Levels/Prime/L05_Prime.lean b/server/testgame/TestGame/Levels/Prime/L05_Prime.lean
deleted file mode 100644
index 61497bd..0000000
--- a/server/testgame/TestGame/Levels/Prime/L05_Prime.lean
+++ /dev/null
@@ -1,42 +0,0 @@
-import TestGame.Metadata
-import Mathlib.Data.Nat.Prime
-
-import Std.Tactic.RCases
-import Mathlib.Tactic.LeftRight
-import Mathlib.Tactic.Contrapose
-import Mathlib.Tactic.Use
-import Mathlib.Tactic.Ring
-
-import TestGame.ToBePorted
-
-Game "TestGame"
-World "Prime"
-Level 3
-
-Title "Primzahlen"
-
-Introduction
-"
-Mathematisch gesehen, bedeutet die Definition von vorhin dass $p$ ein
-irreduzibles Element ist, und Primzahlen sind oft durch
-`∀ (a b : ℕ), p ∣ a * b → p ∣ a ∨ p ∣ b`
-definiert. Auf den natürlichen Zahlen, sind die beiden äquivalent.
-"
-
-Statement
-"Zeige dass $p \\ge 2$ eine Primzahl ist, genau dann wenn
-$p \\mid a\\cdot b \\Rightarrow (p \\mid a) \\lor (p \\mid b)$."
-    (p : ℕ) (h₂ : 2 ≤ p):
-    Nat.Prime p ↔ ∀ (a b : ℕ), p ∣ a * b → p ∣ a ∨ p ∣ b := by
-  constructor
-  intro h a b
-  apply (Nat.Prime.dvd_mul h).mp
-  intro h
-  rw [Nat.prime_iff]
-  change p ≠ 0 ∧ ¬IsUnit p ∧ ∀ a b, p ∣ a * b → p ∣ a ∨ p ∣ b
-  rw [Nat.isUnit_iff, ←and_assoc]
-  constructor
-  constructor
-  linarith
-  linarith
-  assumption
diff --git a/server/testgame/TestGame/Levels/SetFunction.lean b/server/testgame/TestGame/Levels/SetFunction.lean
deleted file mode 100644
index bf9cfbc..0000000
--- a/server/testgame/TestGame/Levels/SetFunction.lean
+++ /dev/null
@@ -1,8 +0,0 @@
-import TestGame.Levels.SetFunction.L01_Image
-import TestGame.Levels.SetFunction.L02_Preimage
-import TestGame.Levels.SetFunction.L03_Range
-import TestGame.Levels.SetFunction.L04_ImageUnion
-
-Game "TestGame"
-World "SetFunction"
-Title "Abbildungen 2"
diff --git a/server/testgame/TestGame/Levels/SetTheory.lean b/server/testgame/TestGame/Levels/SetTheory.lean
deleted file mode 100644
index 0f9a789..0000000
--- a/server/testgame/TestGame/Levels/SetTheory.lean
+++ /dev/null
@@ -1,43 +0,0 @@
-import TestGame.Levels.SetTheory.L01_Univ
-import TestGame.Levels.SetTheory.L02_Empty
-import TestGame.Levels.SetTheory.L03_Subset
-import TestGame.Levels.SetTheory.L04_SubsetEmpty
-import TestGame.Levels.SetTheory.L05_Empty
-import TestGame.Levels.SetTheory.L06_Nonempty
-import TestGame.Levels.SetTheory.L07_UnionInter
-import TestGame.Levels.SetTheory.L08_UnionInter
-import TestGame.Levels.SetTheory.L09_Complement
-import TestGame.Levels.SetTheory.L10_Morgan
-import TestGame.Levels.SetTheory.L11_SSubset
-import TestGame.Levels.SetTheory.L12_Insert
-import TestGame.Levels.SetTheory.L13_Insert
-import TestGame.Levels.SetTheory.L14_SetOf
-import TestGame.Levels.SetTheory.L15_Powerset
-import TestGame.Levels.SetTheory.L16_Disjoint
-import TestGame.Levels.SetTheory.L17_SetOf
-import TestGame.Levels.SetTheory.L18_SetOf
-import TestGame.Levels.SetTheory.L19_Subtype
-
-
-Game "TestGame"
-World "SetTheory"
-Title "Mengenlehre"
-
-Introduction
-"Der größere der beiden Monde sieht dunkelrot und karg aus. Trotzdem sollen dort nomadische
-Gesellschaften wohnen, die sich in der Einöde zurechtfinden.
-
-Ihr steuert einen der wenigen befestigten Standorte am Fusse eines Berges an.
-
-**Robo**: Die Bevölkerung hier lebt so abgekapselt vom Rest des Universums, dass sie sich
-vermutlich noch viel besser mit alter Sprache und Schrift auskennt.
-
-**Du**: Hoffen wir, dass sie uns weiterhelfen können dieses Buch der Urbilder zu entschlüsseln.
-
-Sofort begrüßt euch eine ältere Frau, die sich als *Mengitte*, die Beschützerin des Mondes,
-vorstellt.
-"
-
-Game "TestGame"
-World "SetTheory2"
-Title "Mehr Mengenlehre"
diff --git a/server/testgame/TestGame/Levels/SetTheory/L01_Univ.lean b/server/testgame/TestGame/Levels/SetTheory/L01_Univ.lean
deleted file mode 100644
index e46618c..0000000
--- a/server/testgame/TestGame/Levels/SetTheory/L01_Univ.lean
+++ /dev/null
@@ -1,60 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Init.Set
-import Mathlib.Tactic.Tauto
-
-set_option tactic.hygienic false
-set_option autoImplicit false
-
-Game "TestGame"
-World "SetTheory"
-Level 1
-
-Title "Mengen"
-
-Introduction
-"
-**Mengitte**: Ich würde leider den Inhalt jenes Buches eh nicht verstehen. Aber der beste Weg für
-euch, dieses zu entschlüsseln ist, euch ausgiebig mit der Bevölkerung hier zu unterhalten.
-Lebt mit ihnen, redet mit ihnen und ihr werdet die Sprache automatisch lernen.
-
-**Mengitte**: Seit aber vorgewarnt, die Leute hier denken ganz viel über Mengen nach,
-womit sie immer *homogene Mengen* meinen. Eine Menge natürlicher Zahlen `{1, 4, 6}` ist
-verständlich, aber sowas wie eine Menge `{(2 : ℕ), {3, 1}, \"e\", (1 : ℂ)}` gibt es hier
-einfach nicht. Punkt.
-
-**Robo**: Als Kontext: Wenn `A` ein beliebiger `Type` ist, dann ist `(U : Set A)` eine Menge
-mit Elementen aus `A`
-
-**Mengitte**: Damit ich weiss, dass ihr euch grundsätzlich mit den Leuten austauschen könnt,
-erklärt mir doch folgendes:
-"
-
-open Set
-
-Statement mem_univ "" {A : Type} (x : A) : x ∈ (univ : Set A) := by
-  trivial
-
-Hint (A : Type) (x : A) : x ∈ (univ : Set A) =>
-"**Du**: Also `A` ist ein `Type`, `x` ist ein Element in `A`…
-
-**Robo** … und `univ` ist die Menge aller Elemente in `A`.
-
-**Du** ist das nicht einfach `A` selber?
-
-**Robo** Fast, aber das eine ist ein `Type`, das andere eine Menge, also vom Typ `Set A`.
-
-**Du**: Unlogisch.
-
-**Mengites**: Naja, Typen und Mengen sind halt zwei unterschiedliche Sachen und wenn ihr
-über Mengen sprechen wollt, müssen alles Mengen sein.
-
-**Du**: Na gut. Und wieso `x ∈ univ` und nicht `x : univ` wie bei Typen?
-
-**Robo**: Jedes Element `(x : A)` hat entweder die Eigenschaft `x ∈ U` oder `x ∉ U` für eine
-Menge `(U : Set A)`. (`\\in`, `\\nin`)
-
-**Du**: Also das ist ja dann trivial. Hoffentlich sehen die das hier auch so…
-"
-
-Conclusion "**Mengitte**: Ja das stimmt schon. Dann wünsche ich euch viel Erfolg auf eurer Reise!"
diff --git a/server/testgame/TestGame/Levels/SetTheory/L03_Subset.lean b/server/testgame/TestGame/Levels/SetTheory/L03_Subset.lean
deleted file mode 100644
index a876537..0000000
--- a/server/testgame/TestGame/Levels/SetTheory/L03_Subset.lean
+++ /dev/null
@@ -1,45 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Init.Set
-import Mathlib.Tactic.Tauto
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "SetTheory"
-Level 3
-
-Title "Teilmengen"
-
-Introduction
-"
-Hat man zwei Mengen `(A B : Set ℕ)` kann man fragen, ob diese Teilmengen
-voneinander sind: `A ⊆ B` (`\\sub`/`\\ss`) ist die Notation für Teilmengen, die auch gleich
-sein können.
-
-`A ⊆ B` ist als `∀ x, x ∈ A → x ∈ B` definiert, das heisst, ein `⊆` kann immer auch mit `intro x hx`
-angegangen werden.
-
-Die Taktik `tauto` macht das automatisch, aber um dies zu lernen ist `tauto` hier deaktiviert.
-Benutze also `intro`:
-"
-
-namespace MySet
-
-open Set
-
--- theorem mem_univ {A : Type _} (x : A) : x ∈ (univ : Set A) := by
---   trivial
-
--- theorem not_mem_empty {A : Type _} (x : A) : x ∉ (∅ : Set A) := by
---   tauto
-
-Statement subset_empty_iff
-"." (A : Set ℕ) : A ⊆ univ := by
-  intro h hA
-  trivial --apply mem_univ -- or `trivial`.
-
-NewTactic intro trivial apply
--- blocked: tauto simp
-
-end MySet
diff --git a/server/testgame/TestGame/Levels/Sum.lean b/server/testgame/TestGame/Levels/Sum.lean
deleted file mode 100644
index 3ca27b5..0000000
--- a/server/testgame/TestGame/Levels/Sum.lean
+++ /dev/null
@@ -1,10 +0,0 @@
-import TestGame.Levels.Sum.L01_Simp
-import TestGame.Levels.Sum.L02_Sum
-import TestGame.Levels.Sum.L03_ArithSum
-import TestGame.Levels.Sum.L04_SumOdd
-import TestGame.Levels.Sum.L05_SumComm
-import TestGame.Levels.Sum.L06_Summary
-
-Game "TestGame"
-World "Sum"
-Title "Endliche Summe"
diff --git a/server/testgame/TestGame/Levels/Sum/L01_Simp.lean b/server/testgame/TestGame/Levels/Sum/L01_Simp.lean
deleted file mode 100644
index d7970de..0000000
--- a/server/testgame/TestGame/Levels/Sum/L01_Simp.lean
+++ /dev/null
@@ -1,47 +0,0 @@
-import TestGame.Metadata
-
-import TestGame.Options.BigOperators
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "Sum"
-Level 1
-
-Title "Simp"
-
-Introduction
-"
-In diesem Kapitel lernen wir endliche Summen und mehr Übungen zur Induktion.
-
-Eine endliche Summe läuft erstmal immer über einen endlichen Index
-`Fin n`, welcher $n$ Elemente
-$\\{0, 1, \\ldots, n-1\\}$ beinhaltet.
-
-Der Syntax für  $\\sum_{i=0}^n a_i$ ist `∑ i : Fin n, _` (\\sum)
-
-Als erstes kann die Taktik `simp` (für \"simplification\") ganz viel Triviales vereinfachen.
-`simp` ist eine der stärksten Taktiken in Lean und verwendet
-ganz viele markierte Lemmas um das Goal zu vereinfachen.
-
-Zum Beispiel kennt es ein Lemma das ungefähr so aussieht:
-
-```
-@[simp]
-lemma sum_const_add (n : ℕ) : (∑ i in Fin n, 0) = 0 := by
-  sorry
-```
-
-Die Taktik `simp` benützt alle Lemmas, die mit `@[simp]` markiert sind.
-
-(Tipp: `simp?` zeigt an, welche Lemmas `simp` benutzen würde.)
-"
-
-open BigOperators
-
-Statement
-"Zeige $\\sum_{i = 0} ^ {n-1} (0 + 0) = 0$."
-    (n : ℕ) : (∑ i : Fin n, (0 + 0)) = 0 := by
-  simp
-
-NewTactic simp
diff --git a/server/testgame/TestGame/Levels/Sum/L02_Sum.lean b/server/testgame/TestGame/Levels/Sum/L02_Sum.lean
deleted file mode 100644
index 218187a..0000000
--- a/server/testgame/TestGame/Levels/Sum/L02_Sum.lean
+++ /dev/null
@@ -1,41 +0,0 @@
-import TestGame.Metadata
-
-import TestGame.Options.BigOperators
-import Mathlib
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "Sum"
-Level 2
-
-Title "endliche Summe"
-
-Introduction
-"
-Generell sind aber nur solche Lemmas `@[simp]` markiert, klar eine Vereinfachung darstellen.
-
-So ist ein Lemma wie `Finset.sum_add_distrib` kein `simp`-Lemma, da beide Seiten je
-nach Situation bevorzugt sein könnte:
-
-$$
-  \\sum_{i = 0}^n a_i + b_i = \\sum_{i = 0}^n a_i + \\sum_{j = 0}^n b_j
-$$
-
-Dieses Lemma kann aber mit `rw` angewendet werden.
-"
-
-open BigOperators
-
-Statement
-"Zeige dass $\\sum_{i=0}^{n-1} (i + 1) = n + \\sum_{i=0}^{n-1} i$."
-    (n : ℕ) : ∑ i : Fin n, ((i : ℕ) + 1) = n + (∑ i : Fin n, (i : ℕ)) := by
-  rw [Finset.sum_add_distrib]
-  Hint "Die zweite Summe `∑ x : Fin n, 1` kann `simp` zu `n` vereinfacht werden."
-  simp
-  Hint "Bis auf Umordnung sind jetzt beide Seiten gleich, darum kann `ring` das Goal schließen.
-
-    Alternativ kann man auch mit `rw [add_comm]` dies explizit umordnen."
-  ring
-
-NewLemma Finset.sum_add_distrib add_comm
diff --git a/server/testgame/TestGame/Levels/Sum/L03_ArithSum.lean b/server/testgame/TestGame/Levels/Sum/L03_ArithSum.lean
deleted file mode 100644
index fde2614..0000000
--- a/server/testgame/TestGame/Levels/Sum/L03_ArithSum.lean
+++ /dev/null
@@ -1,92 +0,0 @@
-import TestGame.Metadata
-
-import Mathlib.Algebra.BigOperators.Fin
-import Mathlib.Tactic.Ring
-
-import TestGame.Options.BigOperators
-
-set_option tactic.hygienic false
-
-Game "TestGame"
-World "Sum"
-Level 3
-
-Title "Arithmetische Summe"
-
-Introduction
-"
-Oft beweist man Aussagen über Summen am besten per Induktion.
-
-Mit `induction n` startet man einen Induktionsbeweis. Dies erstellt 2 neue Goals:
-
-* **Induktionsanfang**: `n = 0`. Dieser kann ganz oft direkt mit `simp` bewiesen werden.
-* **Induktionsschritt**: Man kriegt eine Annahme `(n_ih : P n)` und muss `P (n + 1)`
-  beweisen. Für endliche Summen will man normalerweise danach zuerst
-  `rw [Fin.sum_univ_castSucc]` brauchen, welches
-  $$\\sum_{i=0}^{n} a_i = \\sum_{i=0}^{n-1} a_i + a_n$$
-  umschreibt.
-
-**Bemerkung:**
-
-Eine technische Sonderheit bezüglich endlichen Summen
-ist der kleine Pfeil `↑` in `∑ i : Fin (n + 1), ↑i`.
-Da `i : Fin n` technisch keine natürliche Zahl ist (sondern vom Typ `Fin n`), muss man
-dieses zuerst mit `↑i` oder `(i : ℕ)` in eine natürliche Zahl umwandeln. Diese nennt man
-*Coersion*.
-
-Gleichermassen, kommen hier im Induktionsschritt die Terme `↑(↑Fin.castSucc.toEmbedding i)`
-und `↑(Fin.last (n + 1))` vor. Diese Terme können mit `simp` vereinfacht werden.
-"
-
-open BigOperators
-
-Statement arithmetic_sum
-"Zeige $2 \\cdot \\sum_{i = 0}^n i = n \\cdot (n + 1)$."
-    (n : ℕ) : 2 * (∑ i : Fin (n + 1), ↑i) = n * (n + 1) := by
-  induction n
-  simp
-  rw [Fin.sum_univ_castSucc]
-  rw [mul_add]
-  simp
-  rw [n_ih]
-  rw [Nat.succ_eq_add_one]
-  ring
-
-NewTactic induction
-NewLemma Fin.sum_univ_castSucc Nat.succ_eq_add_one mul_add add_mul
-
-Hint (n : ℕ) : 2 * (∑ i : Fin (n + 1), ↑i) = n * (n + 1) =>
-"Als Erinnerung, einen Induktionsbeweis startet man mit `induction n`."
-
-Hint : 2 * ∑ i : Fin (Nat.zero + 1), ↑i = Nat.zero * (Nat.zero + 1) =>
-"Den Induktionsanker $n = 0$ kann `simp` oft beweisen."
-
-Hint (n : ℕ) (hn : 2 * ∑ i : Fin (n + 1), ↑i = n * (n + 1)) :
-  2 * ∑ i : Fin (Nat.succ n + 1), ↑i = Nat.succ n * (Nat.succ n + 1) =>
-"Den Induktionsschritt beginnt man oft mit `rw [Fin.sum_univ_castSucc]`."
-
--- Hint (n : ℕ) (hn : 2 * ∑ i : Fin (n + 1), ↑i = n * (n + 1)) :
---   2 * (∑ i : Fin (n + 1), ↑(Fin.castSucc.toEmbedding i) +
---   ↑(Fin.last (n + 1))) = Nat.succ n * (Nat.succ n + 1) =>
--- "Die Taktik `simp` vereinfacht `↑(↑Fin.castSucc.toEmbedding i)`. "
-
-Hint (n : ℕ) (hn : 2 * ∑ i : Fin (n + 1), ↑i = n * (n + 1)) :
-  2 * (∑ x : Fin (n + 1), ↑x + (n + 1)) = Nat.succ n * (Nat.succ n + 1) =>
-"Um Die Induktionshypothese anzuwenden muss man noch
-$$2 \\cdot ((\\sum_\{x=0}^n x) + (n + 1)) = 2 \\cdot \\sum_\{x=0}^n x + 2 \\cdot (n + 1))$$
-umschreiben. Dazu kannst du `mul_add` benützen.
-"
-
-Hint (n : ℕ) (hn : 2 * ∑ i : Fin (n + 1), ↑i = n * (n + 1)) :
-  2 * ∑ x : Fin (n + 1), ↑x + 2 * (n + 1) = Nat.succ n * (Nat.succ n + 1) =>
-"`simp` vereinfacht `↑(↑Fin.castSucc.toEmbedding i)` zu `↑i`.
-Danach kann die Induktionshypothese mit `rw` angewendet werden."
-
-Hint (n : ℕ) (hn : 2 * ∑ i : Fin (n + 1), ↑i = n * (n + 1)) :
-  n * (n + 1) + 2 * (n + 1) = Nat.succ n * (Nat.succ n + 1) =>
-"
-Im Moment muss man hier `ring` noch helfen,
-indem man mit `rw [Nat.succ_eq_add_one]` zuerst `Nat.succ n = n + 1` umschreibt.
-
-(Dies wird irgendwann noch gefixt)
-"
diff --git a/server/testgame/TestGame/Levels/Sum/L04_SumOdd.lean b/server/testgame/TestGame/Levels/Sum/L04_SumOdd.lean
deleted file mode 100644
index 640072a..0000000
--- a/server/testgame/TestGame/Levels/Sum/L04_SumOdd.lean
+++ /dev/null
@@ -1,58 +0,0 @@
-import TestGame.Metadata
-
-import TestGame.Options.BigOperators
-import Mathlib.Algebra.BigOperators.Fin
-import Mathlib.Tactic.Ring
-
-Game "TestGame"
-World "Sum"
-Level 4
-
-Title "Summe aller ungeraden Zahlen"
-
-Introduction
-"
-Hier nochmals eine Übung zur Induktion.
-"
-set_option tactic.hygienic false
-
-open BigOperators
-
-Statement odd_arithmetic_sum
-"Zeige folgende Gleichung zur Summe aller ungeraden Zahlen:
-
-$\\sum_{i = 0}^n (2n + 1) = n ^ 2$."
-    (n : ℕ) : (∑ i : Fin n, (2 * (i : ℕ) + 1)) = n ^ 2 := by
-  induction' n with n hn
-  simp
-  rw [Fin.sum_univ_castSucc]
-  simp
-  rw [hn]
-  rw [Nat.succ_eq_add_one]
-  ring
-
-HiddenHint (n : ℕ) : (∑ i : Fin n, (2 * (i : ℕ) + 1)) = n ^ 2 =>
-"
-Fange wieder mit `induction {n}` an.
-"
-
-HiddenHint : ∑ i : Fin Nat.zero, ((2 : ℕ) * i + 1) = Nat.zero ^ 2 =>
-"
-Den Induktionsanfang kannst du wieder mit `simp` beweisen.
-"
-
-HiddenHint (n : ℕ) : ∑ i : Fin (Nat.succ n), ((2 : ℕ) * i + 1) = Nat.succ n ^ 2 =>
-"
-Den Induktionsschritt startest du mit `rw [Fin.sum_univ_castSucc]`.
-"
-
-HiddenHint (n : ℕ) (hn : ∑ i : Fin n, (2 * (i : ℕ) + 1) = n ^ 2) :
-  ∑ x : Fin n, (2 * (x : ℕ) + 1) + (2 * n + 1) = Nat.succ n ^ 2 =>
-"
-Hier kommt die Induktionshypothese {hn} ins Spiel.
-"
-
-HiddenHint (n : ℕ) : n ^ 2 + (2 * n + 1) = Nat.succ n ^ 2 =>
-"
-Mit `rw [Nat.succ_eq_add_one]` und `ring` kannst du hier abschliessen.
-"
diff --git a/server/testgame/TestGame/Levels/Sum/L05_SumComm.lean b/server/testgame/TestGame/Levels/Sum/L05_SumComm.lean
deleted file mode 100644
index 957104e..0000000
--- a/server/testgame/TestGame/Levels/Sum/L05_SumComm.lean
+++ /dev/null
@@ -1,36 +0,0 @@
-import TestGame.Metadata
-
-import TestGame.Options.BigOperators
-import Mathlib.Algebra.BigOperators.Fin
-import Mathlib.Tactic.Ring
-
-import TestGame.Options.ArithSum
-
-set_option tactic.hygienic false
-
-open BigOperators
-
-Game "TestGame"
-World "Sum"
-Level 5
-
-Title "Summe vertauschen"
-
-Introduction
-"
-Verschachtelte endliche Summen kann man beliebig tauschen.
-
-$$\\sum_{i=0}^n\\sum_{j=0}^m a_{ij} = \\sum_{j=0}^m\\sum_{i=0}^n a_{ij}$$
-
-Dieses Lemma heisst `Finset.sum_comm`
-"
-
-
-Statement
-"Zeige dass
-$\\sum_{i=0}^n\\sum_{j=0}^m  2^i (1 + j) = \\sum_{j=0}^m\\sum_{i=0}^n  2^i (1 + j)$."
-    (n m : ℕ) : ∑ i : Fin n, ∑ j : Fin m, ( 2^i * (1 + j) : ℕ) =
-    ∑ j : Fin m, ∑ i : Fin n, ( 2^i * (1 + j) : ℕ) := by
-  rw [Finset.sum_comm]
-
-NewLemma Finset.sum_comm
diff --git a/server/testgame/TestGame/Levels/Sum/L06_Summary.lean b/server/testgame/TestGame/Levels/Sum/L06_Summary.lean
deleted file mode 100644
index 7657785..0000000
--- a/server/testgame/TestGame/Levels/Sum/L06_Summary.lean
+++ /dev/null
@@ -1,125 +0,0 @@
-import TestGame.Metadata
-
-import TestGame.Options.BigOperators
-import Mathlib.Algebra.BigOperators.Fin
-import Mathlib.Tactic.Ring
-
-import TestGame.ToBePorted
-import TestGame.Options.ArithSum
-
-Game "TestGame"
-World "Sum"
-Level 6
-
-set_option tactic.hygienic false
-
-Title "Zusammenfassung"
-
-Introduction
-"
-Zusammenfassung aus diesem Kapitel
-
-## Notationen / Begriffe
-
-|                      | Beschreibung                              |
-|:---------------------|:------------------------------------------|
-| `Fin n`              | Ist ein Typ mit Zahlen $0, \\ldots, n-1$. |
-| `∑ (i : Fin n), a i` | $\\sum_{i=0}^{n-1} a_i$                   |
-
-## Taktiken
-
-|    | Taktik                    | Beispiel                             |
-|:---|:--------------------------|:-------------------------------------|
-| 20 | `simp`                    | Simplifikation.                      |
-| 21 | `induction n`             | Induktion über $n$                   |
-
-Und hier noch eine etwas schwierigere Übung.
-
-Das Resultat aus Level 3 kannst du als `arithmetic_sum` wiederverwenden:
-$$
-2 \\cdot \\sum_{i = 0}^n i = n \\cdot (n + 1)
-$$
-"
-
-open BigOperators
-
-Statement
-"Zeige $\\sum_{i = 0}^m i^3 = (\\sum_{i = 0}^m i)^2$."
-  (m : ℕ) : (∑ i : Fin (m + 1), (i : ℕ)^3) = (∑ i : Fin (m + 1), (i : ℕ))^2 := by
-  induction' m with m hm
-  simp
-  rw [Fin.sum_univ_castSucc]
-  simp
-  rw [hm]
-  rw [Fin.sum_univ_castSucc (n := m + 1)]
-  simp
-  rw [add_pow_two]
-  rw [arithmetic_sum]
-  ring
-
-NewLemma arithmetic_sum add_pow_two
-
-HiddenHint (m : ℕ) : ∑ i : Fin (m + 1), (i : ℕ) ^ 3 = (∑ i : Fin (m + 1), ↑i) ^ 2 =>
-"Führe auch hier einen Induktionsbeweis."
-
-HiddenHint : ∑ i : Fin (Nat.zero + 1), (i : ℕ) ^ 3 = (∑ i : Fin (Nat.zero + 1), ↑i) ^ 2 =>
-"`simp` kann den Induktionsanfang beweisen."
-
-Hint (m : ℕ) : ∑ i : Fin (Nat.succ m + 1), (i : ℕ) ^ 3 = (∑ i : Fin (Nat.succ m + 1), ↑i) ^ 2 =>
-"Im Induktionsschritt willst du das Goal so umformen, dass du folgende Therme
-ersetzen kannst:
-
-* `∑ i : Fin (m + 1), ↑i ^ 3` (Induktionshypothese)
-* `2 * (∑ i : Fin (m + 1), ↑i)` (arithmetische Summe)
-"
-
-HiddenHint (m : ℕ) : ∑ i :
-    Fin (Nat.succ m + 1), (i : ℕ) ^ 3 = (∑ i : Fin (Nat.succ m + 1), ↑i) ^ 2 =>
-"
-Als erstes kannst du mal mit dem bekannten `rw [Fin.sum_univ_castSucc]` anfangen.
-"
-
-HiddenHint (m : ℕ) : ∑ i : Fin (m + 1), (Fin.castSucc.toEmbedding i : ℕ) ^ 3 +
-    ↑(Fin.last (m + 1)) ^ 3 = (∑ i : Fin (Nat.succ m + 1), ↑i) ^ 2 =>
-"Mit `simp` kriegst du das `↑(Fin.castSucc.toEmbedding i)` weg"
-
-Hint (m : ℕ) : ∑ x : Fin (m + 1), (x : ℕ) ^ 3 + (m + 1) ^ 3 =
-    (∑ i : Fin (Nat.succ m + 1), ↑i) ^ 2 =>
-"Jetzt kannst du die Induktionshypothese benützen."
-
-Hint (m : ℕ) : (∑ i : Fin (m + 1), (i : ℕ)) ^ 2 + (m + 1) ^ 3 = (∑ i : Fin (Nat.succ m + 1), ↑i) ^ 2 =>
-"Die linke Seite ist jetzt erst mal gut. Um auf der rechten Seite `Fin.sum_univ_castSucc`
-anzuwenden, haben wir ein Problem: Lean schreibt immer die erste Instanz um, also würde gerne
-auf der linken Seite `(∑ i : Fin (m + 1), ↑i) ^ 2` umschreiben.
-
-Wir können Lean hier weiterhelfen, indem wir manche Argemente von `Fin.sum_univ_castSucc`
-explizit angeben. Die Funktion hat ein Argument mit dem Namen `n`, welches wir z.B. explizit
-angeben können:
-
-```
-rw [Fin.sum_univ_castSucc (n := m + 1)]
-```
-"
-
-HiddenHint (m : ℕ) : (∑ i : Fin (m + 1), ↑i) ^ 2 + (m + 1) ^ 3 =
-    (∑ i : Fin (m + 1), ↑(Fin.castSucc.toEmbedding i) + ↑(Fin.last (m + 1))) ^ 2 =>
-"Wenn du noch einen AUsdruck `↑(Fin.castSucc.toEmbedding i)` hast, solltest du mal
-`simp` aufrufen."
-
-Hint (m : ℕ) : (∑ i : Fin (m + 1), ↑i) ^ 2 + (m + 1) ^ 3 = (∑ i : Fin (m + 1), ↑i + (m + 1)) ^ 2 =>
-"Die rechte Seite hat die Form $(a + b)^2$ welche mit `add_pow_two` zu $a^2 + 2ab + b^2$
-umgeschrieben werden kann."
-
-HiddenHint (m : ℕ) : (∑ i : Fin (m + 1), ↑i) ^ 2 + (m + 1) ^ 3 =
-    (∑ i : Fin (m + 1), ↑i) ^ 2 + (2 * ∑ i : Fin (m + 1), ↑i) * (m + 1) + (m + 1) ^ 2 =>
-"Wenn du noch einen AUsdruck `↑(Fin.castSucc.toEmbedding i)` hast, solltest du mal
-`simp` aufrufen."
-
-Hint (m : ℕ) : (∑ i : Fin (m + 1), ↑i) ^ 2 + (m + 1) ^ 3 =
-    (∑ i : Fin (m + 1), ↑i) ^ 2 + (2 * ∑ i : Fin (m + 1), ↑i) * (m + 1) + (m + 1) ^ 2 =>
-"Jetzt hast du in der Mitte `2 * ∑ i : Fin (m + 1), ↑i)`, welches du mit der
-arithmetischen Summe `arithmetic_sum` umschreiben kannst."
-
-Hint (m : ℕ) : (∑ i : Fin (m + 1), ↑i) ^ 2 + (m + 1) ^ 3 =
-    (∑ i : Fin (m + 1), ↑i) ^ 2 + m * (m + 1) * (m + 1) + (m + 1) ^ 2 =>
-"Den Rest sollte `ring` für dich übernehmen."
diff --git a/server/testgame/TestGame/MyNat.lean b/server/testgame/TestGame/MyNat.lean
deleted file mode 100644
index 3cecede..0000000
--- a/server/testgame/TestGame/MyNat.lean
+++ /dev/null
@@ -1,19 +0,0 @@
-axiom MyNat : Type
-
---notation "ℕ" => MyNat
-
---axiom zero : ℕ
-
-axiom succ : ℕ → ℕ
-
-@[instance] axiom MyOfNat (n : Nat) : OfNat ℕ n
-
-@[instance] axiom myAddition : HAdd ℕ ℕ ℕ
-
-@[instance] axiom myMultiplication : HMul ℕ ℕ ℕ
-
-axiom add_zero : ∀ a : ℕ, a + 0 = a
-
-axiom add_succ : ∀ a b : ℕ, a + succ b = succ (a + b)
-
-@[elab_as_elim] axiom myInduction {P : ℕ → Prop} (n : ℕ) (h₀ : P 0) (h : ∀ n, P n → P (succ n)) : P n
diff --git a/server/testgame/TestGame/Options/BigOperators.lean b/server/testgame/TestGame/Options/BigOperators.lean
deleted file mode 100644
index 8a5f1c2..0000000
--- a/server/testgame/TestGame/Options/BigOperators.lean
+++ /dev/null
@@ -1,17 +0,0 @@
-import Mathlib.Algebra.BigOperators.Fin
-
-open BigOperators
-
-open Lean PrettyPrinter Delaborator SubExpr
-
-@[ delab app.Finset.sum]
-def delabFinsetSum : Delab := do
-  guard $ (← getExpr).getAppNumArgs == 5
-  guard $ ((← getExpr).getArg! 3).isAppOf' ``Finset.univ
-  guard $ ((← getExpr).getArg! 4).isLambda
-  withNaryArg 4 do
-    let α ← withBindingDomain delab
-    withBindingBodyUnusedName fun n => do
-      let n : TSyntax `ident := ⟨n⟩
-      let b ← delab
-      `(∑ $n:ident : $α, $b)
diff --git a/server/testgame/TestGame/TacticDocs.lean b/server/testgame/TestGame/TacticDocs.lean
deleted file mode 100644
index 8bd7a6c..0000000
--- a/server/testgame/TestGame/TacticDocs.lean
+++ /dev/null
@@ -1,300 +0,0 @@
-import GameServer.Commands
-
-import TestGame.Tactics
-
-TacticDoc rfl
-"
-## Beschreibung
-
-`rfl` beweist ein Goal der Form `X = X`.
-
-## Detail
-
-`rfl` beweist jedes Goal `A = B` wenn `A` und `B` genau das gleiche sind.
-Wichtig ist nicht, ob diese im Infoview gleich aussehen, sondern ob sie in
-Lean gleich definiert sind.
-
-## Beispiel
-`rfl` kann folgenes Goal beweisen:
-```
-Objects
-  a b c : ℕ
-Prove:
-  (a + b) * c = (a + b) * c
-```
-
-`rfl` kann auch folgendes beweisen:
-```
-Objects
-  n : ℕ
-Prove:
-  1 + 1 = 2
-```
-denn Lean liest dies intern als `0.succ.succ = 0.succ.succ`.
-"
-
-TacticDoc assumption
-"
-## Beschreibung
-
-`assumption` sucht nach einer Annahme, die genau dem Goal entspricht.
-
-## Beispiel
-Wenn das Goal wie folgt aussieht:
-```
-Objects
-  a b c d : ℕ
-  h : a + b = c
-  g : a * b = 16
-  t : c = 12
-Prove:
-  a + b = c
-```
-
-dann findet `assumption` die Annahme `h`und schliesst den Beweis.
-"
-
-TacticDoc rewrite
-"
-## Beschreibung
-
-Wie `rw` aber ruft `rfl` am Schluss nicht automatisch auf.
-"
-
-TacticDoc induction
-"
-## Beschreibung
-
-Wie `rw` aber ruft `rfl` am Schluss nicht automatisch auf.
-"
-
-
-TacticDoc linarith
-"
-## Beschreibung
-
-"
-
-TacticDoc fin_cases
-"
-## Beschreibung
-
-"
-
-TacticDoc funext
-"
-## Beschreibung
-
-"
-
-
-TacticDoc rw
-"
-## Beschreibung
-
-Wenn man eine Annahme `(h : X = Y)` hat, kann man mit
-`rw [h]` alle `X` im Goal durch `Y` ersetzen.
-
-## Detail
-- `rw [←h]` wendet `h` rückwärts an und ersetzt alle `Y` durch `X`.
-- `rw [h, g, ←f]`: Man kann auch mehrere `rw` zusammenfassen.
-- `rw [h] at h₂` ersetzt alle `X` in `h₂` zu `Y` (anstatt im Goal).
-
-`rw` funktioniert gleichermassen mit Annahmen `(h : X = Y)` also auch
-mit Theoremen/Lemmas der Form `X = Y`
-
-## Beispiel
-
-TODO
-"
-
-TacticDoc simp_rw
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc by_cases
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc apply
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc constructor
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc tauto
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc rcases
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc left
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc right
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc simp
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc trivial
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc contradiction
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc push_neg
-"
-## Beschreibung
-
-TODO
-"
-
-
-TacticDoc contrapose
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc revert
-"
-## Beschreibung
-
-TODO
-"
-
-
-TacticDoc by_contra
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc ring
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc unfold
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc use
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc «suffices»
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc «have»
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc «let»
-"
-## Beschreibung
-
-TODO
-"
-
-TacticDoc induction_on
-"
-## Summary
-
-If `n : ℕ` is in our objects list, then `induction_on n`
-attempts to prove the current goal by induction on `n`, with the inductive
-assumption in the `succ` case being `ind_hyp`.
-
-### Example:
-If your current goal is:
-```
-Objects
-  n : ℕ
-Prove:
-  2 * n = n + n
-```
-
-then
-
-`induction_on n`
-
-will give us two goals:
-
-```
-Prove:
-  2 * 0 = 0 + 0
-```
-
-and
-```
-Objects
-  n : ℕ,
-Assumptions
-  ind_hyp : 2 * n = n + n
-Prove:
-  2 * succ n = succ n + succ n
-```
-"
-
-TacticDoc intro
-"Useful to introduce stuff"