Theorem errorBoundedMultExp_aux : forall n1 n2 : Z, (Zabs n1 < Zpos (vNum b))%Z -> (Zabs n2 < Zpos (vNum b))%Z -> (exists ny : Z, (exists ey : Z, (n1 * n2)%R = (ny * powerRZ radix ey)%R :>R /\ (Zabs ny < Zpos (vNum b))%Z)) -> exists nx : Z, (exists ex : Z, (n1 * n2)%R = (nx * powerRZ radix ex)%R :>R /\ (Zabs nx < Zpos (vNum b))%Z /\ (0 <= ex)%Z /\ (ex <= precision)%Z).