proposition: Lemma valid_v_are_in_list: forall g v l x, vvalid (listToGraph' g v l) x -> vvalid g x \/ In x (listVertices (v, l)).
proof: Proof. intros g v l. revert g v. induction l; intros; simpl in *. 1: left; auto. destruct a. specialize (IHl (pregraph_add_whole_edge g e v v0) v0 x H). simpl. clear H. simpl in IHl. unfold addValidFunc in IHl. intuition. 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