intros.
cut (set_In x C \/ set_In x B).
intro; apply set_union_intro.
auto.
cut (set_In x B \/ set_In x C).
tauto.
eapply (set_union_elim (Aeq_dec:=Aeq_dec)).
auto.
Qed.

(* Specifications: *)
Lemma Set_remove2 :
forall (B : set A) (x y : A),
set_In x (set_remove Aeq_dec y B) -> set_In x B.