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

Theorem paradox : forall B:NProp, El B.