proposition: Lemma weak_edge_prop_Union: forall (P Q: V -> Prop) (g: PreGraph V E), Same_set (weak_edge_prop (Union _ P Q) g) (Union _ (weak_edge_prop P g) (weak_edge_prop Q g)).
proof: Proof. intros. unfold weak_edge_prop. rewrite Same_set_spec; intros ?; rewrite !Union_spec. simpl. reflexivity. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.Sets.Ensembles Coq.Sets.Finite_sets Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.relation_list CertiGraph.lib.List_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 Coq.Lists.List CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind