proposition: Lemma aux17: forall e, PE0 e -> root = src g e -> False.
proof: Proof. intros. subst PE0. rewrite Intersection_spec in H; destruct H. unfold weak_edge_prop in H. rewrite <- H0 in H. subst PV0. apply reachable_by_foot_prop in H. subst M_rec M0. apply H. unfold Ensembles.In. rewrite !Union_spec. left; right; auto. 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