open Prod

theorem swap_swap : ∀ x : α × β, swap (swap x) = x
  | ⟨_, _⟩ => by grind

theorem fst_swap {p : α × β} : (swap p).1 = p.2 := by grind

theorem snd_swap {p : α × β} : (swap p).2 = p.1 := by grind