Definition filterintersection : (X → hProp) → hProp := λ A : X → hProp, make_hProp (∏ F, FF F → (pr1 F) A) (impred_isaprop _ (λ _, isapropimpl _ _ (propproperty _))).
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.