proposition: Corollary add_edge_connected_by_path: forall (g: PGraph) e s t p u v, ~ evalid g e -> connected_by_path g p u v -> connected_by_path (pregraph_add_edge g e s t) p u v.
proof: Proof. unfold connected_by_path; intros. split. apply add_edge_valid_upath. auto. apply 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