Suppose $A\in \mathbb R^{m\times n}$ and $b\in \mathbb R^m$, and $A$ is totally unimodular (TUM).
For the system $$Ax\leq b,$$
suppose I use Fourier-Motzkin elimination to eliminate first $k$ variables $(x_1,...,x_k)$, $1\leq k<n$ and obtain the new system
$$A'x'\leq b'$$
Can I show that TUM is closed under Fourier-Motzkin eliminations, i.e. $A'$ is also TU?
