proposition: Lemma is_partial_graph_adj_edge: forall (g1 g2: PGraph) e u v, is_partial_graph g1 g2 -> adj_edge g1 e u v -> adj_edge g2 e u v.
proof: Proof. intros. destruct H0. destruct H0. destruct H2. destruct H. destruct H4. destruct H5. split. split. apply H4; auto. rewrite <- H5; auto. rewrite <- H6; auto. rewrite <- H5; auto. rewrite <- H6; 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