proposition: Lemma edge_spanning_tree_reachable_vvalid_s: forall (g1 g2: Graph) e (P: V -> Prop), edge_spanning_tree g1 e P g2 -> Included (reachable g1 (src g1 e)) (vvalid g2).
proof: Proof. intros. intro y; unfold Ensembles.In; intros. apply reachable_foot_valid in H0. rewrite <- edge_spanning_tree_vvalid_s; eauto. Qed.
imports: Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.relation_list CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation CertiGraph.graph.subgraph2 CertiGraph.graph.reachable_ind Coq.Logic.Classical