intros p q H'.
apply Rle_trans with (Fulp b radix precision q).
apply (ClosestUlp p q); auto.
replace (powerRZ radix (Fexp q)) with (FtoRradix (Float 1%nat (Fexp q))).
apply (FulpLe b radix); auto.
apply
RoundedModeBounded with (radix := radix) (P := Closest b radix) (r := p);
auto.
apply ClosestRoundedModeP with (precision := precision); auto.
unfold FtoRradix, FtoR in |- *; simpl in |- *.
ring.
Qed.

Theorem ClosestErrorExpStrict :
forall (p q : float) (x : R),
Fbounded b p ->
Fbounded b q ->
Closest b radix x p ->
q = (x - p)%R :>R -> q <> 0%R :>R -> (Fexp q < Fexp p)%Z.