proposition: Lemma union_part_prop_rev : forall A : part_set E, in_part A P -> forall x : E, in_part x A -> in_part x union_part.
proof: Proof. unfold union_part in |- *; simpl in |- *; auto with algebra. intros A H' x H'0; try assumption. exists A; split; [ try assumption | idtac ]. auto with algebra. Qed.
imports: Sets