Module NatList.
Inductive natprod : Type :=
| pair : nat -> nat -> natprod.
Instance dec_natprod (p q : natprod) : Dec (p = q).
Admitted. (* QuickChick surjective_pairing. *)
Admitted. (* QuickChick snd_fst_is_swap. *)

Theorem fst_swap_is_snd : forall (p : natprod),
fst (swap_pair p) = snd p.