proposition: Lemma reachable_by_path_merge: forall (g: Gph) p1 n1 n2 p2 n3 P, g |= p1 is n1 ~o~> n2 satisfying P -> g |= p2 is n2 ~o~> n3 satisfying P -> g |= (p1 +++ p2) is n1 ~o~> n3 satisfying P.
proof: Proof. intros. destruct H. destruct H0. split. apply path_ends_glue with n2; auto. apply good_path_merge; auto. eapply path_ends_meet; eauto. 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