Summary: Let \(\boldsymbol{L}\) be a divisible residuated lattice. It is shown that for each \(a\in \boldsymbol{L}\), there is a natural way to make the lattice \(\{x\in \boldsymbol{L}\mid x\leqslant a\}\) a divisible residuated lattice \(\boldsymbol{L}_a\). Furthermore, if \(\boldsymbol{L}\) is prelinear (a generalized MV-algebra), then so is \(\boldsymbol{L}_a\).