Lemma isantisymm_filter_le {X : UU} : ∏ F G : PreFilter X, filter_le F G → filter_le G F → F = G. Proof. intros F G Hle Hge. simple refine (subtypePath_prop (B := λ _, make_hProp _ _) _). - apply isapropdirprod. + apply isaprop_isfilter_imply. + apply isaprop_isfilter_finite_intersection. - apply funextfun ; intros A. apply hPropUnivalence. + now apply Hge. + now apply Hle. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.