proposition: Lemma vertices_at_sepcon_unique_x1 {SGA_vs: PointwiseGraphAssum_vs SGP}: forall (g: Graph) x P d, vertices_at P g * vertex_at x d |-- !! (~ P x).
proof: Proof. intros. apply not_prop_right; intros. eapply derives_trans; [apply sepcon_derives; [apply pred_sepcon_prop_true; eauto | apply derives_refl] |]. unfold graph_vcell. rewrite sepcon_comm, <- sepcon_assoc. eapply derives_trans; [apply sepcon_derives; [apply vertex_at_sep | apply derives_refl] |]. normalize. 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