compiling and tutorial world approx finished

Game/MyNat/Addition.lean

@@ -5,16 +5,19 @@ namespace MyNat
 open MyNat
 
 def add : MyNat → MyNat → MyNat
-  | a, 0   => a
+  | a, zero  => a
   | a, MyNat.succ b => MyNat.succ (MyNat.add a b)
 
-instance : Add MyNat where
+instance instAdd : Add MyNat where
   add := MyNat.add
 
 /--
-This theorem proves that if you add zero to a MyNat you get back the same number.
+`add_zero a` is a proof of `a + 0 = a`.
+
+`add_zero` is a `simp` lemma, because if you see `a + 0`
+you usually want to simplify it to `a`.
 -/
-theorem add_zero (a : MyNat) : a + 0 = a := by rfl
+@[simp] 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.

Game/MyNat/AdvAddition.lean

@@ -7,6 +7,6 @@ example (a b : ℕ) (h : (succ a) = b) : succ (succ a) = succ b := by
   simp
   sorry
 
-axiom succ_inj {a b : ℕ} : succ a = succ b → a = b
+--axiom succ_inj {a b : ℕ} : succ a = succ b → a = b
 
-axiom zero_ne_succ (a : ℕ) : 0 ≠ succ a
+--axiom zero_ne_succ (a : ℕ) : 0 ≠ succ a

Game/MyNat/DecidableEq.lean

@@ -1,4 +1,4 @@
-import Game.Levels.Tutorial.L02rw-- makes simps work?
+import Game.MyNat.Addition-- makes simps work?
 import Mathlib.Tactic
 namespace MyNat
 
@@ -51,7 +51,7 @@ We need to learn how to deal wiht a goal of the form `P → Q`
 
 -/
 
-theorem succ_inj (a b : ℕ) (h : succ a = succ b) : a = b := by
+theorem succ_inj {a b : ℕ} (h : succ a = succ b) : a = b := by
   apply_fun pred at h
   simpa
 
@@ -90,7 +90,7 @@ congrArg pred
 -/
 @[simp] theorem succ_eq_succ_iff : succ a = succ b ↔ a = b := by
   constructor
-  · exact succ_inj a b
+  · exact succ_inj
   · simp
 
 /-