proposition: Lemma EST_not_reachable_derive: forall (g1 : Graph) (e : E) (P : V -> Prop) (g2 : Graph) (x y : V), edge_spanning_tree g1 e P g2 -> ~ g1 |= dst g1 e ~o~> y satisfying P -> ~ reachable g1 x y -> ~ reachable g2 x y.
proof: Proof. intros. destruct H as [[? ?] | [? ?]]. + intro. apply H1. apply (spanning_tree_not_reachable_derive g1 (dst g1 e) P g2 x y); auto. + apply (gremove_not_reachable_derive g1 e g2 x y); auto. 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