replace V1' with (map injgauche V1).
intros.
elimtype (exists y : Elt, dans y V1 /\ S' = (fun e : Elt => couple e zero) y).
intros x temp; elim temp; clear temp.
intros dans_x_V1 S_egal.
absurd (S' = couple x zero).
unfold S', zero in |- *.
discriminate.
auto.
apply (dans_map (fun e : Elt => couple e zero)).
assumption.
unfold V1' in |- *.
simpl in |- *.
auto.
Qed.
Hint Resolve N_dans_S_V1'.

(* Specifications: *)
Lemma N_dans_S_V2' : ~ dans S' V2'.
red in |- *.