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