rintro ⟨hn, hp⟩ m hm
p : ℕ → ℕ
n : ℕ
ih : 0 < rec 1 (fun n ih => (p n).pos.and ih) n ↔ ∀ m < n, 0 < p m
⊢ (0 < p n ∧ ∀ m < n, 0 < p m) → ∀ m ≤ n, 0 < p m
case intro
p : ℕ → ℕ
n : ℕ
ih : 0 < rec 1 (fun n ih => (p n).pos.and ih) n ↔ ∀ m < n, 0 < p m
hn : 0 < p n
hp : ∀ m < n, 0 < p m
m : ℕ
hm : m ≤ n
⊢ 0 < p m