proposition: Lemma list_edges_evalid_iff: forall g v l e, evalid g e \/ In e (listEdges' Vertex Edge l) <-> evalid (listToGraph' g v l) e.
proof: Proof. intros; split; intros. + destruct H; [apply listToGraph'_preserve_evalid | apply list_edges_evalid]; auto. + apply (valid_e_are_in_list _ v); 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