unfold extension in |- *.
intros e f x N_dans_x_e.
elim (extension_spec e f x).
intro; tauto.
Qed.
Section fonctions2.
Variable E : Ensf.
Variable F : Ensf.
Variable f : Elt -> Elt.
Hint Unfold application.

Lemma is_epi_f_over_image : is_epi E (map f E) f.
split.