more levels.

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

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+import Mathlib.Algebra.BigOperators.Basic
+import Mathlib
+
+import TestGame.Metadata
+
+set_option tactic.hygienic false
+
+Game "TestGame"
+World "Induction"
+Level 1
+
+Title "Summe"
+
+Introduction
+"
+"
+
+Statement
+""
+    (n : ℕ) : 2 * (∑ i : Fin (n+1), ↑i) = n * (n + 1) := by
+  induction' n with n hn
+  simp
+  sorry -- done in Lean3.
+
+Tactics intro constructor assumption

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

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+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