proposition: Lemma valid_path_strong_evalid: forall g v p e, valid_path g (v, p) -> In e p -> strong_evalid g e.
proof: Proof. intros g v p. revert v. induction p; intros. 1: inversion H0. simpl in H0. destruct H0. + subst. destruct H. simpl in H0. destruct p; intuition. + apply valid_path_cons in H. specialize (IHp _ _ H H0). 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