proposition: Lemma list_edges_evalid: forall g v l e, In e (listEdges' Vertex Edge l) -> evalid (listToGraph' g v l) e.
proof: Proof. intros. revert g v H. induction l; simpl; intros. 1: exfalso; auto. destruct a. simpl in H. destruct H. + subst. apply listToGraph'_preserve_evalid, addEdge_add_evalid. + apply IHl. 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