proposition: Lemma GSG_PartialGraphPreserve2: forall P1 P2 (G1 G2: LabeledGraph V E DV DE DG), Included P1 (vguard G1) -> Included P2 (vguard G2) -> Included P1 (vvalid G1) -> Included P2 (vvalid G2) -> ((predicate_partial_labeledgraph G1 P1) ~=~ (predicate_partial_labeledgraph G2 P2))%LabeledGraph -> vertices_identical2 P1 P2 (Graph_PointwiseGraph G1) (Graph_PointwiseGraph G2).
proof: Proof. intros. assert (Same_set P1 P2). + destruct H3 as [[? _] _]. rewrite Same_set_spec; unfold pointwise_relation. simpl in H3; unfold predicate_vvalid in H3. unfold Included, Ensembles.In in H1, H2. firstorder. + rewrite <- H4 in *. split; auto. apply GSG_PartialGraphPreserve; 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