  We show that maximal $S$-free convex sets are polyhedra when $S$ is the set
of integral points in some rational polyhedron of $\mathbb{R}^n$. This result
extends a theorem of Lov\'asz characterizing maximal lattice-free convex sets.
Our theorem has implications in integer programming. In particular, we show
that maximal $S$-free convex sets are in one-to-one correspondence with minimal
inequalities.
