proposition: Lemma edge_spanning_tree_left_vvalid: forall (g1 g2: Graph) x n, vvalid g1 x -> edge_spanning_tree g1 (x, L) g2 -> (vvalid g1 n <-> vvalid g2 n).
proof: Proof. intros. apply (edge_spanning_tree_vvalid g1 g2 (x, L) n); 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