fact: Definition uf_union (g1: PreGraph Vertex Edge) (e1 e2: Vertex) (g2: PreGraph Vertex Edge) : Prop := forall (S1 S2: uf_set), S1 e1 -> S2 e2 -> uf_set_in g1 S1 -> uf_set_in g1 S2 -> uf_set_in g2 (Union Vertex S1 S2) /\ (forall S, ~ Same_set S S1 -> ~ Same_set S S2 -> uf_set_in g1 S -> uf_set_in g2 S) /\ (forall S, uf_set_in g2 S -> Same_set S (Union Vertex S1 S2) \/ uf_set_in g1 S).
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