proposition: Lemma localDag_graph_gen_step_list: forall (g: Graph) x S d, vvalid g x -> localDag g x -> step_list g x S -> Included (reachable_through_set g S) (vguard g) -> Included (reachable_through_set g S) (vguard (labeledgraph_vgen g x d)) -> reachable_through_vertices_at S g = reachable_through_vertices_at S (labeledgraph_vgen g x d).
proof: Proof. intros. apply va_reachable_through_partialgraph_eq; auto. split; [reflexivity | split; intros; [| reflexivity]]. simpl. unfold update_vlabel. destruct_eq_dec x v; [exfalso | auto]. destruct (localDag_reachable_spec g x S H H0 H1). destruct H4. symmetry in H6; revert H6. apply H8; 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