proposition: Lemma is_list_edge_dst_the_same: forall root s d v, is_list root -> reachable g root s -> g |= s ~> d -> g |= s ~> v -> d = v.
proof: Proof. intros. destruct H1 as [? [? ?]]. destruct H2 as [? [? ?]]. rewrite step_spec in H4, H6. destruct H4 as [e1 [? [? ?]]]. destruct H6 as [e2 [? [? ?]]]. subst v d. assert (e1 = e2) by (apply (is_list_same_src_same_edge root s e1 e2); auto). subst e1. 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