intros B x n H' H'0; try assumption.
apply cardinal_S with B x; auto with *.
unfold not in |- *; intros.
cut (~ in_part x (single x)).
unfold not in |- *; auto with *.
apply diff_in_r with B; auto with *.
Qed.
Hint Resolve cardinal_minus_part: algebra.

Lemma tiroirs :
forall (n : nat) (Chaussettes : part_set E),
cardinal Chaussettes n ->
forall (m : nat) (Tiroirs : part_set F),
cardinal Tiroirs m ->
m < n ->
(forall x : E, in_part x Chaussettes -> in_part (f x) Tiroirs) ->
exists x : E, (exists y : E, ~ Equal x y /\ Equal (f x) (f y)).