exact ⟨
by rintro ⟨hn, hp⟩ m hm; rcases lt_or_eq_of_le hm with (hm | rfl); { exact hp _ hm }; { exact hn },
by intro h; exact ⟨h n (Nat.le_refl n), fun m hm => h m (le_of_lt hm)⟩⟩
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
no goals