named Statements are added to context with there specified name

2023-04-14 10:48:46 +02:00
parent 0560c0100b
commit b1dc4d71b3
12 changed files with 37 additions and 73 deletions
@@ -8,14 +8,6 @@ Title "add_assoc (associativity of addition)"

 open MyNat

-theorem MyNat.zero_add (n : ℕ) : 0 + n = n := by
-  induction n with n hn
-  · rw [add_zero]
-    rfl
-  · rw [add_succ]
-    rw [hn]
-    rfl
-
 Introduction
 "
 It's well-known that $(1 + 2) + 3 = 1 + (2 + 3)$; if we have three numbers
@@ -8,17 +8,6 @@ Title "succ_add"

 open MyNat

-theorem MyNat.add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c)  := by
-  induction c with c hc
-  · rw [add_zero]
-    rw [add_zero]
-    rfl
-  · rw [add_succ]
-    rw [add_succ]
-    rw [add_succ]
-    rw [hc]
-    rfl
-
 Introduction
 "
 Oh no! On the way to `add_comm`, a wild `succ_add` appears. `succ_add`
@@ -8,16 +8,6 @@ Title "`add_comm` (boss level)"

 open MyNat

-theorem MyNat.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]
-    rw [add_succ]
-    rfl
-
 Introduction
 "
 [boss battle music]
@@ -9,16 +9,6 @@ Title "succ_eq_add_one"

 open MyNat

-theorem MyNat.add_comm (a b : ℕ) : a + b = b + a := by
-  induction b with d hd
-  · rw [zero_add]
-    rw [add_zero]
-    rfl
-  · rw [add_succ]
-    rw [hd]
-    rw [succ_add]
-    rfl
-
 theorem one_eq_succ_zero : (1 : ℕ) = succ 0 := by simp only

 NewLemma MyNat.one_eq_succ_zero