intro
| Or.inl h => exact Nat.succ_lt_succ h
| Or.inr h => absurd h; apply Nat.succ_ne_zero
case succ_succ.mp
x y : Nat
a✝ : x - 1 < y ∨ x = 0 ↔ x < y + 1
⊢ x + 1 - 1 < y + 1 ∨ x + 1 = 0 → x + 1 < y + 1 + 1
no goals