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