Section fonctions2.
Variable E : Ensf.
Variable F : Ensf.
Variable f : Elt -> Elt.
Hint Unfold application.
split.
auto.
intros.
cut (exists y : Elt, dans y E /\ x = f y :>Elt).
intro temp; elim temp; clear temp.
intro. intuition.
prolog [ ex_intro2 ] 4.
(*Intros y temp; Elim temp; Clear temp ; Intros dans_y egal_y. Exists y;Auto.*)
auto.
Qed.
Hint Resolve is_epi_f_over_image.

Lemma mono_imp_iso_over_image : is_mono E f -> is_iso E (map f E) f.