Lemma isasetPreFilter (X : UU) : isaset (PreFilter X). Proof. simple refine (isaset_carrier_subset (make_hSet _ _) (λ _, make_hProp _ _)). - apply impred_isaset ; intros _. apply isasethProp. - apply isapropdirprod. + apply isaprop_isfilter_imply. + apply isaprop_isfilter_finite_intersection. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.