  We prove that the asymptotics of the Fredholm determinant of $I-K_\alpha$,
where $K_\alpha$ is the integral operator with the sine kernel
$\sin(x-y)/(x-y)/\pi$ on the interval $[0,\alpha]$ is given by a formula which
was conjectured by F.J. Dyson. The first and second order asymptotics as well
as the higher order asymptotics except for the constant term have already been
proved. In this paper we thus determine the constant term.
