nng

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

@@ -8,7 +8,9 @@ Title "add_assoc (associativity of addition)"
 
 open MyNat
 
-theorem MyNat.zero_add (n : ℕ) : 0 + n = n := by
+namespace AdditionWorld
+
+theorem zero_add (n : ℕ) : 0 + n = n := by
   induction n with n hn
   · rw [add_zero]
     rfl

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

@@ -9,7 +9,9 @@ Title "succ_add"
 
 open MyNat
 
-theorem MyNat.add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
+namespace AdditionWorld
+
+theorem add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
   induction c with c hc
   · rw [add_zero]
     rw [add_zero]
@@ -20,7 +22,6 @@ theorem MyNat.add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
     rw [hc]
     rfl
 
-
 Introduction
 "
 Oh no! On the way to `add_comm`, a wild `succ_add` appears. `succ_add`
@@ -52,6 +53,7 @@ $ \\operatorname{succ}(a) + b = \\operatorname{succ}(a + b)$."
     Hint "Induction on `a` will not work."
   induction b with d hd
   · rw [add_zero]
+    rw [add_zero]
     rfl
   · rw [add_succ]
     rw [hd]

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

@@ -9,9 +9,12 @@ Title "`add_comm` (boss level)"
 
 open MyNat
 
-theorem MyNat.succ_add (a b : ℕ) : succ a + b = succ (a + b)  := by
+namespace AdditionWorld
+
+theorem succ_add (a b : ℕ) : succ a + b = succ (a + b)  := by
   induction b with d hd
   · rw [add_zero]
+    rw [add_zero]
     rfl
   · rw [add_succ]
     rw [hd]

server/nng/NNG/Levels/Addition/Level_5.lean

@@ -9,7 +9,9 @@ Title "succ_eq_add_one"
 
 open MyNat
 
-theorem MyNat.add_comm (a b : ℕ) : a + b = b + a := by
+namespace AdditionWorld
+
+theorem add_comm (a b : ℕ) : a + b = b + a := by
   induction b with d hd
   · rw [zero_add]
     rw [add_zero]
@@ -19,8 +21,7 @@ theorem MyNat.add_comm (a b : ℕ) : a + b = b + a := by
     rw [succ_add]
     rfl
 
-theorem MyNat.one_eq_succ_zero : (1 : ℕ) = succ 0 := by
-  rfl
+theorem one_eq_succ_zero : (1 : ℕ) = succ 0 := by simp only
 
 NewLemma MyNat.add_comm MyNat.one_eq_succ_zero
 

server/nng/NNG/Levels/Addition/Level_6.lean

@@ -9,11 +9,13 @@ Title "add_right_comm"
 
 open MyNat
 
+namespace AdditionWorld
+
 Introduction
 "
 Lean sometimes writes `a + b + c`. What does it mean? The convention is
 that if there are no brackets displayed in an addition formula, the brackets
-are around the left most `+` (Lean's addition is \"left associative\"). 
+are around the left most `+` (Lean's addition is \"left associative\").
 So the goal in this level is `(a + b) + c = (a + c) + b`. This isn't
 quite `add_assoc` or `add_comm`, it's something you'll have to prove
 by putting these two theorems together.