proposition: Lemma Disjoint_x1: forall {U} {UE: EqDec U eq} (A B: Ensemble U) (x0: U), Disjoint U (fun x: U => A x /\ x0 <> x) B -> ~ B x0 -> Disjoint U A B.
proof: Proof. intros. rewrite Disjoint_spec in H |- *. intros. specialize (H x). destruct_eq_dec x0 x; [subst |]; tauto. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Equivalence Coq.Sets.Ensembles Coq.Sets.Constructive_sets CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext