p q : Prop,
Hp : p
⊢ q ∨ p

p q : Prop,
Hq : q
⊢ q ∨ p
-----
⊢ 0 = 0 ∨ 0 = succ (pred 0)

n' : ℕ,
Hind : n' = 0 ∨ n' = succ (pred n')
⊢ succ n' = 0 ∨ succ n' = succ (pred (succ n'))
-----
H : 0 ≠ 0
⊢ 0 > 0 → 0 = succ (pred 0)

a : ℕ,
ih_1 : a ≠ 0 → a > 0 → a = succ (pred a),
H : succ a ≠ 0
⊢ succ a > 0 → succ a = succ (pred (succ a))