fact: Definition finite_intersection {X : UU} (P : Sequence (X → hProp)) : X → hProp.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Combinatorics.FiniteSequences UniMath.Foundations.NaturalNumbers UniMath.Tactics.EnsureStructuredProofs