fact: Definition Choice_type := forall (X Y : HSet) (R : X -> Y -> HProp), (forall x, hexists (R x)) -> hexists (fun f => forall x, R x (f x)).
imports: HoTT(ExcludedMiddle abstract_algebra) HoTT(HIT.unique_choice) HoTT(Spaces.Card) HoTT.Sets(Ordinals)