Record Fbound : Set := Bound {vNum : positive; dExp : N}.Record Fbound : Set := Bound {vNum : positive; dExp : N}.Record Fbound : Set := Bound {vNum : positive; dExp : N}.Record Fbound : Set := Bound {vNum : positive; dExp : N}.Definition Fbounded (b : Fbound) (d : float) :=
  (Zabs (Fnum d) < Zpos (vNum b))%Z /\ (- dExp b <= Fexp d)%Z.

Theorem Zle_monotony_contra_abs_pow : forall x y z n : Z, (0 < z)%Z -> (Rabs (x * powerRZ z n) <= Rabs (y * powerRZ z n))%R -> (Zabs x <= Zabs y)%Z.