intros n m p; case p; unfold Fshift in |- *; simpl in |- *.
intros Fnum1 Fexp1; apply floatEq; simpl in |- *; auto with zarith.
rewrite Zpower_nat_is_exp; auto with zarith.
rewrite (Zmult_comm (Zpower_nat radix n)); auto with zarith.
rewrite <- (Zminus_plus_simpl_r (Fexp1 - m) n m).
replace (Fexp1 - m + m)%Z with Fexp1; auto with zarith.
replace (Z_of_nat (n + m)) with (n + m)%Z; auto with zarith arith.
rewrite <- inj_plus; auto.
Qed.

Theorem ReqGivesEqwithSameExp :
forall p q : float,
exists r : float,
(exists s : float, p = r :>R /\ q = s :>R /\ Fexp r = Fexp s).