proposition: Lemma filterbase_notempty : isfilter_notempty filterbase.
proof: Proof. intros A. apply hinhuniv. intros B. generalize (Hfalse _ (pr1 (pr2 B))). apply hinhfun. intros x. exists (pr1 x). apply (pr2 (pr2 B)), (pr2 x). Qed.
imports: UniMath.Foundations.Preamble UniMath.MoreFoundations.Tactics UniMath.Topology.Prelim UniMath.MoreFoundations.PartA