proposition: Corollary add_edge_connected: forall (g: PGraph) e s t u v, ~ evalid g e -> connected g u v -> connected (pregraph_add_edge g e s t) u v.
proof: Proof. intros. destruct H0 as [p ?]. exists p. apply add_edge_connected_by_path; auto. 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