Theorem ClosestErrorBoundNormal2_aux : forall (x : R) (p : float), Closest b radix x p -> Fnormal radix b p -> Fnormal radix b (Fnormalize radix b precision (FPred b radix precision p)) -> (0 < x)%R -> (x < p)%R -> (Rabs (x - p) <= Rabs x * (/ 2%nat * powerRZ radix (Zsucc (- precision))))%R.