  Let $\Lambda\subset\mathbf{R}^{n}$ be a lattice which contains the integer
lattice $\mathbf{Z}^{n}$. We characterize the space of linear functions
$\mathbf{R}^{n}\rightarrow\mathbf{R}$ which vanish on the lattice points of
$\Lambda$ lying in the half-open unit cube $[0,1)^{n}$. We also find an
explicit formula for the dimension of the linear span of
$\Lambda\cap[0,1)^{n}$. The results in this paper generalize and are based on
the Terminal Lemma of Reid, which is in turn based upon earlier work of
Morrison and Stevens on the classification of four dimensional isolated
Gorenstein terminal cyclic quotient singularities.
