(** We show that h, which is f on J and g elsewhere, is a bijection *)
(** Theorem: h_bij (bijection U A B h) *)

(* Specifications: *)
Theorem h_bij : bijection U A B h.
(** h is from A to B *)
Lemma h1 : Rel U A B h.
(** h satisfies to_at_most_one_output *)
Lemma h2 : to_at_most_one_output U h.
(** h satisfies to_at_least_one_output *)
Lemma h3 : to_at_least_one_output U A h.
(** h satisfies from_at_most_one_input *)
Lemma h4 : from_at_most_one_input U h.
(** h satisfies from_at_least_one_input *)
Lemma h5 : from_at_least_one_input U B h.
End Bijection.