Definition andp {worlds: Type} (X: Ensemble worlds) (Y: Ensemble worlds): Ensemble worlds :=
  fun m => X m /\ Y m.Definition orp {worlds: Type} (X: Ensemble worlds) (Y: Ensemble worlds): Ensemble worlds :=
  fun m => X m \/ Y m.Definition falsep {worlds: Type}: Ensemble worlds := fun m => False.

Lemma falsep_closed {worlds: Type} {R: Relation worlds}: upwards_closed_Kdenote falsep.