intros x y z H'; apply Rmult_le_reg_l with (r := powerRZ radix z);
auto with real zarith.
repeat rewrite (Rmult_comm (powerRZ radix z)); auto.
Qed.

(* Specifications: *)
Theorem FtoREqInv1 :
forall p q : float, ~ is_Fzero p -> p = q :>R -> Fnum p = Fnum q -> p = q.