Lemma filterim_notempty : isfilter_notempty filterim. Proof. intros A Fa. generalize (Hempty _ Fa). apply hinhfun. intros x. exists (f (pr1 x)). exact (pr2 x). Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.