proposition: Lemma totally_unmarked_root_ST_reachable_eq: forall (g1 g2: Graph) root, totally_unmarked g1 root -> spanning_tree g1 root g2 -> vertices_at (reachable g1 root) g2 = reachable_vertices_at root g2.
proof: Proof. intros. apply vertices_at_Same_set. rewrite Same_set_spec. hnf. apply spanning_tree_totally_unmarked_root_reachable; auto. intros. apply Graph_reachable_by_dec, weak_valid_vvalid_dec; right; auto. Qed.
imports: VST.msl.seplog VST.msl.log_normalize CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.EquivDec_ext Coq.Lists.List CertiGraph.msl_ext.ramification_lemmas CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation CertiGraph.graph.subgraph2 CertiGraph.graph.reachable_ind CertiGraph.graph.spanning_tree CertiGraph.graph.BinGraph CertiGraph.graph.MathGraph CertiGraph.graph.FiniteGraph CertiGraph.msl_application.Graph CertiGraph.msl_application.GraphBin CertiGraph.msl_application.GraphBin_Mark