proposition: Lemma BaseOfPreFilter_and {X : UU} (base : BaseOfPreFilter X) : ∏ A B : X → hProp, base A → base B → ∃ C : X → hProp, base C × (∏ x, C x → A x ∧ B x).
proof: Proof. apply (pr1 (pr2 base)). Qed.
imports: UniMath.Foundations.Preamble UniMath.MoreFoundations.Tactics UniMath.Topology.Prelim UniMath.MoreFoundations.PartA