rename testgame to adam

server/adam/Adam/Levels/Induction/L01_Induction.lean

@@ -0,0 +1,37 @@
+import TestGame.Metadata
+
+import Mathlib
+
+set_option tactic.hygienic false
+
+Game "TestGame"
+World "Induction"
+Level 1
+
+Title "Induktion"
+
+Introduction
+"
+Dieses Kapitel enthält noch ein paar Übungen zur Induktion.
+"
+
+Statement
+"Zeige dass $5^n + 7$ durch $4$ teilbar ist."
+    (n : ℕ) : 4 ∣ 5^n + 7 := by
+  induction n
+  simp
+  rcases n_ih
+  rw [Nat.pow_succ, Nat.mul_succ, add_assoc, h, mul_comm, ←mul_add]
+  simp
+
+--NewLemma Nat.pow_succ, Nat.mul_succ, add_assoc, mul_comm, ←mul_add
+
+-- example (n : ℕ) : Even (n^2 + n) := by
+--   induction n
+--   simp
+--   rw [Nat.succ_eq_add_one]
+--   rcases n_ih with ⟨x, h⟩
+--   use x + n_1 + 1
+--   ring_nf at *
+--   rw [←h]
+--   ring