proposition: Lemma choose_3: forall s s' x y, choose s = Some x -> choose s' = Some y -> Equal s s' -> E.eq x y.
proof: Proof. intros s s' x y Hx Hy H. apply choose_3' in H. congruence. Qed.
imports: Bool PeanoNat BinPos OrderedType OrderedTypeEx FSetInterface