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