proposition: Lemma PreFilterBase_Generated {X : UU} (base : BaseOfPreFilter X) : PreFilterBase base = PreFilterGenerated base.
proof: Proof. simple refine (subtypePath_prop (B := λ _, make_hProp _ _) _). - apply isapropdirprod. + apply isaprop_isfilter_imply. + apply isaprop_isfilter_finite_intersection. - simpl. apply filterbase_genetated. + intros A B. apply (BaseOfPreFilter_and base). + apply (BaseOfPreFilter_notempty base). Qed.
imports: UniMath.Foundations.Preamble UniMath.MoreFoundations.Tactics UniMath.Topology.Prelim UniMath.MoreFoundations.PartA