proposition: Lemma vertices_at_sepcon_x1: forall (g: Graph) x P P' d, Prop_join P (eq x) P' -> vgamma g x = d -> vertices_at P g * vertex_at x d = vertices_at P' g.
proof: Proof. intros. subst d. change (vertex_at x (vgamma g x)) with (graph_vcell g x). destruct H. symmetry; apply pred_sepcon_sepcon1. + firstorder. + firstorder. 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