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

Theorem Rle_monotony_contra_exp :
forall (x y : R) (z : Z),
(x * powerRZ radix z <= y * powerRZ radix z)%R -> (x <= y)%R.