proposition: Lemma aux09: Disjoint _ PE1_root PE0.
proof: Proof. intros. rewrite H_PE0. rewrite Disjoint_spec. intros e ? ?. rewrite Intersection_spec in H0. unfold weak_edge_prop in H0. rewrite aux04 in H0 by auto. destruct H0. generalize (@eq_refl _ root) H0. generalize root at 2 3. rewrite <- Disjoint_spec. apply aux08. Qed.
imports: CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.EquivDec_ext CertiGraph.lib.relation_list CertiGraph.lib.Morphisms_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation CertiGraph.graph.subgraph2 CertiGraph.graph.graph_morphism