Theorem ClosestPropHigham25 : forall (x : R) (p : float), Closest b radix x p -> exists delta : R, (exists nu : R, (x / (1 + delta) + nu)%R = FtoRradix p /\ (Rabs delta <= / 2%nat * powerRZ radix (Zsucc (- precision)))%R /\ (Rabs nu <= / 2%nat * powerRZ radix (- dExp b))%R /\ (delta * nu)%R = 0%R /\ (Fnormal radix b (Fnormalize radix b precision p) -> nu = 0%R) /\ (Fsubnormal radix b (Fnormalize radix b precision p) -> delta = 0%R)).