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