Degree-one generation condition for Proj

If a nonnegatively graded ring $S$ is generated by $S_1$ as an $S_0$-algebra, the standard affine opens of Proj $D_{+}(f)$ with $f\in S_1$ cover $\mathrm{Proj}S$. Indeed a homogeneous prime containing every degree-one element would contain the irrelevant ideal of a graded ring. This condition makes all twisting sheaves on Proj invertible and makes graded sheafification compatible with tensor products of sheaves.