(** The paradoxical set *)
Definition U := forall P:Prop, pow P.(** Bijection between [U] and [(pow U)] *)
Definition f (u:U) : pow U := u U.Definition g (h:pow U) : U :=
  fun X => let lX := j2 (L1 X U) in let rU := i2 (L1 U U) in lX (rU h).

(* Specifications: *)
Lemma retract_pow_U_U : retract (pow U) U.