proposition: Lemma filtersubtype_notempty : isfilter_notempty filtersubtype.
proof: 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.
imports: UniMath.Foundations.Preamble UniMath.MoreFoundations.Tactics UniMath.Topology.Prelim UniMath.MoreFoundations.PartA