proposition: Lemma Empty_set_iff: forall U x, Ensembles.In U (Empty_set U) x <-> False.
proof: Proof. intros; split; intro; inversion H. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Equivalence Coq.Sets.Ensembles Coq.Sets.Constructive_sets CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext