intros x dans_x_V1.
unfold injproducg, extension in |- *.
elim (extension_spec V1 injgauche x).
intros x0 temp; elim temp; clear temp; intro temp; elim temp; clear temp.
auto.
intros.
absurd (dans x V1); assumption.
Qed.
Hint Resolve injproducg_V1.

Lemma map_injproducg_V1 : map (injproducg V1) V1 = map injgauche V1 :>Ensf.
apply map_egal.