Section Paradox.
(** ** Retract of [Prop] in a small type *)
(** The retract is axiomatized using logical equivalence as the equality on propositions. *)
Variable bool : Prop.
Variable p2b : Prop -> bool.
Variable b2p : bool -> Prop.
Hypothesis p2p1 : forall A:Prop, b2p (p2b A) -> A.
Hypothesis p2p2 : forall A:Prop, A -> b2p (p2b A).
(** ** Paradox *)

Theorem paradox : forall B:Prop, B.