Theorem errorBoundedMultExpPos : forall P, RoundedModeP b radix P -> forall p q pq : float, Fbounded b p -> Fbounded b q -> (0 <= p)%R -> (0 <= q)%R -> P (p * q)%R pq -> (- dExp b <= Fexp p + Fexp q)%Z -> ex (fun r : float => ex (fun s : float => Fbounded b r /\ Fbounded b s /\ r = pq :>R /\ s = (p * q - r)%R :>R /\ Fexp s = (Fexp p + Fexp q)%Z :>Z /\ (Fexp s <= Fexp r)%Z /\ (Fexp r <= precision + (Fexp p + Fexp q))%Z)).