Theorem errorBoundedMultClosest : forall p q pq : float, Fbounded b p -> Fbounded b q -> Closest b radix (p * q) pq -> (- dExp b <= Fexp p + Fexp q)%Z -> (- dExp b <= Fexp (Fnormalize radix b precision pq) - precision)%Z -> ex (fun r : float => ex (fun s : float => Fcanonic radix b r /\ Fbounded b r /\ Fbounded b s /\ r = pq :>R /\ s = (p * q - r)%R :>R /\ Fexp s = (Fexp r - precision)%Z :>Z)).