proposition: Lemma list_vertices_vvalid_iff: forall g v l x, vvalid g v -> (vvalid g x \/ In x (listVertices (v, l)) <-> vvalid (listToGraph' g v l) x).
proof: Proof. intros. split; intros. + destruct H0; [apply listToGraph'_preserve_vvalid | apply list_vertices_vvalid]; auto. + apply valid_v_are_in_list; 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