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