proposition: Lemma aux13: forall e, PE1 e -> PV0 (dst g e) -> False.
proof: Proof. intros. subst PV0. pose proof reachable_by_foot_valid _ _ _ _ H0. apply reachable_by_foot_prop in H0. subst PE1 M_rec. unfold weak_edge_prop in H. rewrite Intersection_spec in H; destruct H. apply H0. unfold Ensembles.In. right. subst PV1. apply reachable_by_through_set_step with (src g e); auto. + intro; apply H0. unfold Ensembles.In. rewrite Union_spec; left; auto. + exists e; 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