(** We show that h, which is f on J and g elsewhere, is a bijection *)

    Inductive h (x y : U) : Prop :=
      | hl_intro : In U J x -> f x y -> h x y
      | hr_intro : Setminus U B (Imf J) y -> g y x -> h x y.(** We show that h, which is f on J and g elsewhere, is a bijection *)

    Inductive h (x y : U) : Prop :=
      | hl_intro : In U J x -> f x y -> h x y
      | hr_intro : Setminus U B (Imf J) y -> g y x -> h x y.(** We show that h, which is f on J and g elsewhere, is a bijection *)

    Inductive h (x y : U) : Prop :=
      | hl_intro : In U J x -> f x y -> h x y
      | hr_intro : Setminus U B (Imf J) y -> g y x -> h x y.

Lemma h2 : to_at_most_one_output U h.