intros z H'; repeat (split; simpl in |- *; auto with zarith).
rewrite pGivesBound; auto.
apply Zlt_le_trans with (Zpower_nat radix 1); auto with zarith.
rewrite Zpower_nat_1; auto with zarith.
Qed.

Theorem FboundedMboundPos :
forall z m : Z,
(0 <= m)%Z ->
(m <= Zpower_nat radix precision)%Z ->
(- dExp b <= z)%Z ->
exists c : float, Fbounded b c /\ c = (m * powerRZ radix z)%R :>R.