more levels.

server/testgame/TestGame.lean

@@ -5,8 +5,7 @@ import TestGame.Levels.Implication
 import TestGame.Levels.Predicate
 import TestGame.Levels.Contradiction
 import TestGame.Levels.Prime
-
+import TestGame.Levels.Induction
-import TestGame.Levels.Naturals.L31_Sum
 
 Game "TestGame"
 
@@ -65,4 +64,4 @@ Conclusion
 
 Path Proposition → Implication → Predicate → Contradiction
 Path Predicate → Prime
-Path Predicate → Nat2
+Path Predicate → Induction

server/testgame/TestGame/Levels/Contradiction/L01_Have.lean

@@ -47,7 +47,8 @@ Message (A : Prop) (B : Prop) (h : A → ¬ B) (g : A ∧ B) : False =>
 "
 
 Message (A : Prop) (B : Prop) (h : A → ¬ B) (g : A) (f : B) : False =>
-" Auf Deutsch: \"Als Zwischenresultat haben wir `¬ B`.\"
+"
+Auf Deutsch: \"Als Zwischenresultat haben wir `¬ B`.\"
 
 In Lean :
 
@@ -57,8 +58,8 @@ Message (A : Prop) (B : Prop) (h : A → ¬ B) (g : A) (f : B) : False =>
 ```
 "
 
-example (n : ℕ) : n.succ + 2 = n + 3 := by
+-- example (n : ℕ) : n.succ + 2 = n + 3 := by
-ring_nf
+-- ring_nf
 
 Conclusion ""
 

server/testgame/TestGame/Levels/Contradiction/L06_Summary.lean

@@ -7,7 +7,7 @@ import Mathlib.Tactic.Ring
 import TestGame.ToBePorted
 
 Game "TestGame"
-World "Proving"
+World "Contradiction"
 Level 6
 
 Title "Contradiction"

server/testgame/TestGame/Levels/Induction.lean

@@ -0,0 +1,2 @@
+import TestGame.Levels.Induction.L31_Sum
+import TestGame.Levels.Induction.L32_Induction

server/testgame/TestGame/Levels/Induction/L31_Sum.lean

@@ -6,7 +6,7 @@ import TestGame.Metadata
 set_option tactic.hygienic false
 
 Game "TestGame"
-World "Nat2"
+World "Induction"
 Level 1
 
 Title "Summe"
@@ -16,7 +16,7 @@ Introduction
 "
 
 Statement
-"Zeige $\\sum_{i=0}^{n} i = \\frac{n \\cdot {n+1}}{2}$"
+""
     (n : ℕ) : 2 * (∑ i : Fin (n+1), ↑i) = n * (n + 1) := by
   induction' n with n hn
   simp

server/testgame/TestGame/Levels/Induction/L32_Induction.lean

@@ -0,0 +1,37 @@
+import TestGame.Metadata
+import Mathlib.Tactic.Ring
+import Mathlib
+
+Game "TestGame"
+World "Induction"
+Level 2
+
+Title "Induktion"
+
+Introduction
+"
+TODO: Induktion (& induktion vs rcases)
+
+"
+
+
+theorem nat_succ (n : ℕ) : Nat.succ n = n + 1 := rfl
+
+lemma hh1 (n m : ℕ) (h : 2 * m = n) : m = n / 2 := by
+  rw [←h]
+  rw [Nat.mul_div_right]
+  simp
+
+Statement
+"Zeige $\\sum_{i = 0}^n i = \\frac{n ⬝ (n + 1)}{2}$."
+  (n : ℕ) : (∑ i : Fin (n + 1), ↑i) = n * (n + 1) / 2 := by
+  apply hh1
+  induction' n with n hn
+  simp
+  sorry
+  -- rw [Fin.sum_univ_castSucc]
+  -- simp [nat_succ]
+  -- rw [mul_add, hn]
+  -- ring
+
+Tactics ring

server/testgame/TestGame/Levels/Naturals/L32_Induction.lean

@@ -1,23 +0,0 @@
-import TestGame.Metadata
-import Mathlib.Tactic.Ring
-
-Game "TestGame"
-World "Nat2"
-Level 2
-
-Title "Induktion"
-
-Introduction
-"
-TODO: Induktion (& induktion vs rcases)
-
-"
-
-Statement "" : True := by
-  trivial
-
-Conclusion
-"
-"
-
-Tactics ring