proposition: Lemma reachable_by_edge: forall (g: Gph) n1 n2 n3 (P: Ensemble V), P n3 -> g |= n1 ~o~> n2 satisfying P -> g |= n2 ~> n3 -> g |= n1 ~o~> n3 satisfying P.
proof: Proof. intros. apply reachable_by_trans with n2; auto. apply reachable_by_foot_prop in H0. apply edge_P_reachable_by; auto. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.micromega.Lia CertiGraph.lib.Coqlib CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.graph.graph_model Coq.Lists.List Coq.Lists.ListDec