proposition: Lemma add_edge_valid_upath: forall (g: PGraph) e s t p, ~ evalid g e -> valid_upath g p -> valid_upath (pregraph_add_edge g e s t) p.
proof: Proof. induction p; intros. auto. destruct p. auto. split. destruct H0. destruct H0. exists x. apply add_edge_adj_edge2; auto. unfold not; intros; subst x. destruct H0. destruct H0. contradiction. apply IHp. auto. apply H0. Qed.
imports: Coq.Logic.Classical CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_relation CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.FiniteGraph