proposition: Lemma pregraph_join_vvalid_mono: forall PV PE G1 G2, pregraph_join PV PE G1 G2 -> forall v: V, vvalid G1 v -> vvalid G2 v.
proof: Proof. intros. rewrite pregraph_join_iff in H. destruct H as [? _]. destruct H. rewrite H. auto. 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 CertiGraph.graph.graph_gen