proposition: Lemma add_edge_fits_upath: forall (g: PGraph) e s t p l, ~ evalid g e -> fits_upath g l p -> fits_upath (pregraph_add_edge g e s t) l p.
proof: Proof. induction p; intros. destruct l; auto. destruct l. auto. destruct p. auto. split. destruct H0. destruct (EE e e0). unfold equiv in e1; subst e0. destruct H0. destruct H0. contradiction. unfold complement, equiv in c. apply add_edge_adj_edge2; auto. apply IHp. apply H. apply fits_upath_cons in H0. 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