(** Encoding of Russel's paradox *)

(** The boolean negation. *)
Definition Not_b (b:Bool) := IFProp (b = T) F T.(** the set of elements not belonging to itself *)
Definition R : U := g (fun u:U => Not_b (u U u)).

(* Specifications: *)
Lemma not_has_fixpoint : R R = Not_b (R R).
Theorem classical_proof_irrelevance : T = F.