proposition: Lemma uf_equiv_union_equiv: forall (g1 g2 g: Graph) x y, uf_equiv g1 g2 -> uf_union g1 x y g <-> uf_union g2 x y g.
proof: Proof. intros. split; intro; [apply (uf_equiv_union g2 g1); auto; apply uf_equiv_sym | apply (uf_equiv_union g1 g2)]; auto. 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