induction c with
| zero => rfl
| succ n hn =>
  rw [mul_succ, mul_succ, hn, mul_succ, add_assoc, add_assoc]
  congr 1
  rw [← add_assoc, add_comm _ a, add_assoc]
S : Type
image_zero : S
image_succ : N → S → S
a b c : N
⊢ (a + b) * c = a * c + b * c
no goals