Variant bijective : Prop := Bijective g of cancel f g & cancel g f.Variant bijective : Prop := Bijective g of cancel f g & cancel g f.

(* Specifications: *)
Lemma bij_inj : injective f.
Lemma bij_can_sym f' : cancel f' f <-> cancel f f'.
Lemma bij_can_eq f' f'' : cancel f f' -> cancel f f'' -> f' =1 f''.
Lemma eq_bij : bijective f -> forall g, f =1 g -> bijective g.
Lemma bij_comp : bijective f -> bijective h -> bijective (f \o h).
Lemma bij_can_bij : bijective f -> forall f', cancel f f' -> bijective f'.