  We prove that the defining ideal of a sufficiently high Veronese subring of a
toric algebra admits a quadratic Gr\"obner basis consisting of binomials. More
generally, we prove that the defining ideal of a sufficiently high Veronese
subring of a standard graded ring admits a quadratic Gr\"obner basis. We give a
lower bound on $d$ such that the defining ideal of $d$-th Veronese subring
admits a quadratic Gr\"obner basis. Eisenbud--Reeves--Totaro stated the same
theorem without a proof with some lower bound on $d$. In many cases, our lower
bound is less than Eisenbud--Reeves--Totaro's lower bound.
