proposition: Lemma uf_equiv_root_the_same: forall (g1 g2: UFGraph) x root, uf_equiv g1 g2 -> uf_root g1 x root <-> uf_root g2 x root.
proof: Proof. intros. pose proof (@uf_equiv_the_same_root _ _ _ _ _ _ _ _ out_edge isNullDec fml g1 g2 x root H). apply H0. Qed.
imports: Coq.Sets.Ensembles Coq.Lists.List CertiGraph.lib.EquivDec_ext CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_computable CertiGraph.graph.graph_gen CertiGraph.graph.FiniteGraph CertiGraph.graph.MathGraph CertiGraph.graph.LstGraph CertiGraph.graph.UnionFind