Definition opair_of_sum (s : T1 + T2) :=
  match s with inl x => (Some x, None) | inr y => (None, Some y) end.

(* Specifications: *)
Lemma opair_of_sumK : pcancel opair_of_sum sum_of_opair.
Lemma bool_of_unitK : cancel (fun _ => true) (fun _ => tt).