Lemma BaseOfPreFilter_notempty {X : UU} (base : BaseOfPreFilter X) : ∃ A : X → hProp, base A. Proof. apply (pr2 (pr2 base)). Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.