intros P H' p q H'0; case (H' p q); auto; intros H'1.
apply FminRep with (3 := pGivesBound); auto with arith.
apply FmaxRep with (3 := pGivesBound); auto with arith.
Qed.

(* Specifications: *)
Theorem RoundedModeRep :
forall P,
RoundedModeP P ->
forall p q : float, P p q -> exists m : Z, q = Float m (Fexp p) :>R.