Lemma filtersubtype_imply : isfilter_imply filtersubtype. Proof. intros A B Himpl. apply Himp. intros x Ax Hx. apply Himpl, Ax. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.