Section ListSetLemmas.
Variable A : Set.
Hypothesis Aeq_dec : forall x y : A, {x = y} + {x <> y}.
intros.
cut (set_In x B \/ set_In x C).
intro H1; elim H1.
tauto.
auto.
eapply (set_union_elim (Aeq_dec:=Aeq_dec)); auto.
Qed.

Lemma Set_union2 :
forall (B C : set A) (x : A),
set_In x (set_union Aeq_dec B C) -> set_In x (set_union Aeq_dec C B).