simp[ih]
case succ
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 ∧ 0 < rec 1 (fun n ih => (p n).pos.and ih) n ↔ ∀ m ≤ n, 0 < p m
case succ
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