proposition: Lemma is_list_no_self_edge: forall root s, is_list root -> reachable g root s -> g |= s ~> s -> False.
proof: Proof. intros. apply (is_list_no_edge_loop root s s); auto. apply reachable_foot_valid in H0. apply reachable_refl; auto. Qed.
imports: Coq.Classes.Morphisms Coq.micromega.Lia Coq.Logic.FunctionalExtensionality CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.FiniteGraph