proposition: Lemma vertices_at_vertices_identical2: forall (g1 g2: Graph) (P1 P2: V -> Prop), vertices_identical2 P1 P2 g1 g2 -> vertices_at P1 g1 = vertices_at P2 g2.
proof: Proof. intros. apply pred_sepcon_strong_proper. + destruct H. rewrite Same_set_spec in H; auto. + intros. unfold graph_vcell. f_equal. destruct H. rewrite vertices_identical_spec in H2. apply H2; auto. Qed.
imports: Coq.Logic.Classical VST.msl.seplog VST.msl.log_normalize VST.msl.ramification_lemmas CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.Relation_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.Morphisms_ext CertiGraph.msl_ext.log_normalize CertiGraph.msl_ext.iter_sepcon CertiGraph.msl_ext.ramification_lemmas CertiGraph.msl_ext.abs_addr CertiGraph.msl_ext.seplog CertiGraph.graph.graph_model CertiGraph.graph.graph_gen CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_computable CertiGraph.graph.reachable_ind CertiGraph.graph.subgraph2 CertiGraph.graph.dag CertiGraph.graph.FiniteGraph