Lemma filterintersection_imply : isfilter_imply filterintersection. Proof. intros A B H Ha F Hf. apply (Himp F Hf A). - apply H. - simple refine (Ha _ _). exact Hf. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.