Definition boxp {worlds: Type} {R: KM.Relation worlds} (X: Ensemble worlds): Ensemble worlds :=
  fun m => forall n, KM.Krelation m n -> X n.

Lemma boxp_closed {worlds: Type} {R1: KI.Relation worlds} {po_R1: PreOrder KI.Krelation} {R2: KM.Relation worlds} {ukmM: UpwardsClosedOrderedKripkeModel worlds}: forall (X: Ensemble worlds), upwards_closed_Kdenote X -> upwards_closed_Kdenote (boxp X).