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

State before:
S : Type
image_zero : S
image_succ : N → S → S
n m a b c : N
⊢ succ a + b = succ (a + b)
Tactic:
induction b with
| zero =>
  rfl
| succ b hb =>
  rw [add_succ, add_succ, hb]
State after:
no goals

State before:
case zero
S : Type
image_zero : S
image_succ : N → S → S
n m a b c : N
⊢ succ a + zero = succ (a + zero)
Tactic:
rfl
State after:
no goals

State before:
case succ
S : Type
image_zero : S
image_succ : N → S → S
n m a b✝ c b : N
hb : succ a + b = succ (a + b)
⊢ succ a + succ b = succ (a + succ b)
Tactic:
rw [add_succ, add_succ, hb]
State after:
no goals