proposition: Lemma EST_the_same_dst: forall (P: V -> Prop) g1 root g2 (e1 e2 : E), e1 <> e2 -> ~ P root -> out_edges g1 root e2 -> edge_spanning_tree g1 e1 P g2 -> dst g1 e2 = dst g2 e2.
proof: Proof. intros. destruct H2 as [[? ?] | [? ?]]. + destruct H3 as [? _]. eapply ppg_the_same_dst; eauto. + destruct H3 as [? [? [? [? ?]]]]. assert (e2 <> e1) by intuition. specialize (H4 _ H8). specialize (H6 _ H8). destruct H1. apply H6; intuition. Qed.
imports: Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.relation_list CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation CertiGraph.graph.subgraph2 CertiGraph.graph.reachable_ind Coq.Logic.Classical