intros b p q H' H'0.
case (Rle_or_lt (Fexp q) (Fexp p)); intros H'1.
exists p; repeat (split; auto).
exists q; split; [ idtac | split ]; auto with real.
apply FboundedEqExp with (p := p); auto.
apply Rlt_le; auto.
Qed.

Theorem FboundedShiftLess :
forall (b : Fbound) (f : float) (n m : nat),
m <= n -> Fbounded b (Fshift radix n f) -> Fbounded b (Fshift radix m f).