Lemma filternat_notempty : isfilter_notempty filternat. Proof. intros A. apply hinhfun. intros N. exists (pr1 N). apply (pr2 N (pr1 N)). now apply isreflnatleh. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.