fact: Definition TotallyBoundedSubset := forall (e:Qpos), {l : list X | forall y, In y l -> P y & forall x, P x -> exists y, In y l /\ ball (proj1_sig e) x y }.
imports: CoRN.model.totalorder.QposMinMax CoRN.metric2.Limit CoRN.metric2.FinEnum Coq.ZArith.Zpow_facts CoRN.metric2.Complete CoRN.logic.Classic Coq.QArith.Qpower Coq.QArith.Qround