Lemma BaseOfFilter_notempty {X : UU} (base : BaseOfFilter X) : ∃ A : X → hProp, base A. Proof. apply (pr1 (pr2 (pr2 base))). Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.