proposition: Lemma ultra_cvg_clusterE (T : topologicalType) (F : set_system T) : UltraFilter F -> cluster F = [set p | F --> p].
proof: Proof. move=> FU; rewrite predeqE => p; split. by rewrite cluster_cvgE => - [G GF [cvGp /max_filter <-]]. by move=> cvFp; rewrite cluster_cvgE; exists F; [apply: ultra_proper|split]. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed