intros.
inversion H1.
rewrite <- H0.
rewrite <- H4.
apply cardinal_empty.
apply Trans with A; auto with algebra.
rewrite <- H0.
rewrite <- H6.
apply cardinal_add with B0 x; auto with algebra.
apply Trans with A; auto with algebra.
Qed.
Hint Resolve cardinal_comp: algebra.

(* Specifications: *)
Lemma cardinal_comp_l :
forall (A B : part_set E) (n : nat),
Equal A B -> cardinal A n -> cardinal B n.