Lemma filterdom_notempty : isfilter_notempty filterdom. Proof. intros. intros A Fa. generalize (Hdom _ Fa). apply hinhfun. intros x. exists (pr1 x). apply (pr2 (pr2 x)), (pr1 (pr2 x)). Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.