proposition: Lemma gremove_not_reachable_derive: forall (g1 : Graph) (e : E) (g2 : Graph) (x y : V), gremove_edge g1 e g2 -> ~ reachable g1 x y -> ~ reachable g2 x y.
proof: Proof. intros. intro. apply H0; clear H0. destruct H1 as [p ?]. exists p. apply (gremove_not_reachable_by_derive _ e g2); 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