Theorem: N.one_mul (LeanTeaching/TD/TD02_sol.lean)

State before:
S : Type
image_zero : S
image_succ : N → S → S
a b c : N
⊢ 1 * a = a
Tactic:
induction a with
| zero => rfl
| succ n hn =>
  rw [mul_succ, hn, one_eq_succ_zero, add_succ, add_zero]
State after:
no goals

State before:
case zero
S : Type
image_zero : S
image_succ : N → S → S
a b c : N
⊢ 1 * zero = zero
Tactic:
rfl
State after:
no goals

State before:
case succ
S : Type
image_zero : S
image_succ : N → S → S
a b c n : N
hn : 1 * n = n
⊢ 1 * succ n = succ n
Tactic:
rw [mul_succ, hn, one_eq_succ_zero, add_succ, add_zero]
State after:
no goals