Theorem errorBoundedMultNeg : forall P, RoundedModeP b radix P -> forall p q f : float, Fbounded b p -> Fbounded b q -> (p <= 0)%R -> (0 <= q)%R -> (- dExp b <= Fexp p + Fexp q)%Z -> P (p * q)%R f -> exists r : float, r = (p * q - f)%R :>R /\ Fbounded b r /\ Fexp r = (Fexp p + Fexp q)%Z.