proposition: Lemma ufroot_same_false: forall a b a_rt b_rt, uf_root g a a_rt -> uf_root g b b_rt -> a_rt <> b_rt -> ufroot_same a b -> False.
proof: Proof. intros. destruct H2 as [? [? ?]]. apply H1. pose proof (uf_root_unique _ _ _ H2 H). pose proof (uf_root_unique _ _ _ H3 H0). rewrite <- H4, H5; trivial. Qed.
imports: CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.lib.Ensembles_ext CertiGraph.lib.EnumEnsembles CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.MathGraph CertiGraph.graph.LstGraph CertiGraph.graph.FiniteGraph CertiGraph.graph.reachable_computable