proposition: Lemma acyclic_path_cons: forall (g: Gph) links s a, valid_path g (s, a :: links) -> acyclic_path g (s, a :: links) -> acyclic_path g (dst g a, links).
proof: Proof. intros. red in H0 |- *. rewrite epath_to_vpath_cons_eq in H0. apply NoDup_cons_1 with (x := s); trivial. destruct H; trivial. 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