proposition: Lemma the_same_root_union: forall (g g1 g2: UFGraph) x y root, vvalid g x -> vvalid g y -> uf_equiv g g1 -> uf_equiv g1 g2 -> uf_root g1 x root -> uf_root g2 y root -> uf_union g x y g2.
proof: Proof. intros. apply (same_root_union g g1 g2 x y root); auto. 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