case intro.zero
m n k : ℕ
p : ℕ → Prop
hn : p zero
⊢ p 0 ∨ ∃ n, p (n + 1)

case intro.succ
m n✝ k : ℕ
p : ℕ → Prop
n : ℕ
hn : p (succ n)
⊢ p 0 ∨ ∃ n, p (n + 1)
m n k : ℕ
p : ℕ → Prop
⊢ (∃ n, p n) → p 0 ∨ ∃ n, p (n + 1)
rintro ⟨_ | n, hn⟩
no goals
case intro.zero
m n k : ℕ
p : ℕ → Prop
hn : p zero
⊢ p 0 ∨ ∃ n, p (n + 1)

case intro.succ
m n✝ k : ℕ
p : ℕ → Prop
n : ℕ
hn : p (succ n)
⊢ p 0 ∨ ∃ n, p (n + 1)
exacts [Or.inl hn, Or.inr ⟨n, hn⟩]