nng levels

server/nng/NNG/Levels/Tutorial/Level_2.lean

@@ -4,31 +4,29 @@ import NNG.MyNat.Multiplication
 Game "NNG"
 World "Tutorial"
 Level 2
-Title "the rewrite (rw) tactic"
+Title "the 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.
+The \"rewrite\" tactic `rw` 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.)*
+Here is a theorem which cannot be proved using rfl -- you need a rewrite first.
 "
 
 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`.
+  Hint "You can use `rw [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 "Not all hints are directly shown. If you are stuck and need more 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

server/nng/NNG/Levels/Tutorial/Level_3.lean

@@ -40,13 +40,13 @@ 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`:
+Now let us practise the use of `rw` 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`.
+  Hint "You can use `rw` and your assumption `{h}` to substitute `succ a` with `b`.
 
   Notes:
 
@@ -54,7 +54,7 @@ Statement
   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]`."
+  before `h` like this: `rw [← h]`."
   Branch
     rewrite [← h]
     Hint (hidden := true) "Now both sides are identical…"

server/nng/NNG/Levels/Tutorial/Level_4.lean

@@ -21,9 +21,9 @@ 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
+Even better, you can use the `rw` tactic
 with `add_zero`. If you ever see `x + 0` in your goal,
-`rewrite [add_zero]` should simplify it to `x`. This is
+`rw [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).
@@ -38,23 +38,24 @@ What's going on here is that we assume `a + d` is already defined, and we define
 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.
+`rw [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`
+  Hint "You find `{a} + succ …` in the goal, so you can use `rw` and `add_succ`
   to make progress."
-  Hint (hidden := true) "Explicitely, type `rewrite [add_succ]`!"
-  rewrite [add_succ]
+  Hint (hidden := true) "Explicitely, type `rw [add_succ]`!"
+  rw [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) "Explicitely, type `rw [add_zero]`!"
+  rw [add_zero]
   Hint (hidden := true) "Finally both sides are identical."
   rfl
 
 NewLemma MyNat.add_succ MyNat.add_zero
+NewDefinition Add
 
 Conclusion
 "