proposition: Lemma good_path_split: forall (g: Gph) p1 p2 P, paths_meet g p1 p2 -> good_path g P (p1 +++ p2) -> (good_path g P p1) /\ (good_path g P p2).
proof: Proof. intros. destruct H0. apply path_prop_split in H1; auto. destruct H1. apply valid_path_split in H0; auto. destruct H0. unfold good_path. split; split; 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