intros Fnum1 Fexp1 Fnum2 Fexp2 H' H'0; rewrite H'0; rewrite H'0 in H'.
cut (Fnum1 = Fnum2).
intros H'1; rewrite <- H'1; auto.
apply eq_IZR; auto.
apply Rmult_eq_reg_l with (r := powerRZ radix Fexp1);
repeat rewrite (Rmult_comm (powerRZ radix Fexp1));
auto.
apply Rlt_dichotomy_converse; right; auto with real.
red in |- *; auto with real.
Qed.

Theorem FshiftFdigit :
forall (n : nat) (x : float),
~ is_Fzero x -> Fdigit (Fshift n x) = Fdigit x + n.