proposition: Lemma add_edge_adj_edge1: forall (g: PGraph) e s d, vvalid g s -> vvalid g d -> adj_edge (pregraph_add_edge g e s d) e s d.
proof: Proof. unfold adj_edge; intros. split. apply add_edge_strong_evalid; auto. rewrite add_edge_src. rewrite add_edge_dst. left; 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