intros x y e H.
simple inversion H.
left.
injection H1.
intros.
apply trans_equal with x0; [ auto | assumption ].
intro.
right.
injection H2.
intros.
rewrite <- H3.
rewrite <- H1.
assumption.
Qed.

Lemma dans_add_contr :
forall (x y : Elt) (e : Ensf), y <> x -> ~ dans x e -> ~ dans x (add y e).