proposition: Lemma vertices_at_ramif_1_stable: forall (g: Graph) (P: V -> Prop) x d, vgamma g x = d -> P x -> vertices_at P g |-- vertex_at x d * (vertex_at x d -* vertices_at P g).
proof: Proof. intros. apply vertices_at_ramif_1. eexists. split; [| split]. + apply Ensemble_join_Intersection_Complement. - unfold Included, Ensembles.In; intros; subst. auto. - intros. apply decidable_prop_decidable. apply equiv_dec. + apply Ensemble_join_Intersection_Complement. - unfold Included, Ensembles.In; intros; subst. auto. - intros. apply decidable_prop_decidable. apply equiv_dec. + reflexivity. + auto. + 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