Definition Fweight (p : float) :=
  (Fnum p + Fexp p * Zpower_nat radix precision)%Z.

Theorem FinductPosAux : forall (P : float -> Prop) (p : float), (0 <= p)%R -> Fcanonic radix b p -> P p -> (forall q : float, Fcanonic radix b q -> (p <= q)%R -> P q -> P (FSucc b radix precision q)) -> forall x : Z, (0 <= x)%Z -> forall q : float, x = (Fweight q - Fweight p)%Z -> Fcanonic radix b q -> (p <= q)%R -> P q.