Fourier–Motzkin消去法
( ⋀ h c h ≤ a h x ) ∧ ( ⋀ i c i < a i x ) ∧ ( ⋀ j b j x ≤ d j ) ∧ ( ⋀ k b k x < d k ) {\displaystyle \exists x.\left(\bigwedge _{h}c_{h}\leq a_{h}x\right)\land \left(\bigwedge _{i}c_{i}<a_{i}x\right)\land \left(\bigwedge _{j}b_{j}x\leq d_{j}\right)\land \left(\bigwedge _{k}b_{k}x<d_{k}\right)} ⇔ ( ⋀ h , j b j c h ≤ a h d j ) ∧ ( ⋀ h , k b k c h < a h d k ) ∧ ( ⋀ i , j b j c i < a i d j ) ∧ ( ⋀ i , k b k c i < a i d k ) {\displaystyle \Leftrightarrow \left(\bigwedge _{h,j}b_{j}c_{h}\leq a_{h}d_{j}\right)\land \left(\bigwedge _{h,k}b_{k}c_{h}<a_{h}d_{k}\right)\land \left(\bigwedge _{i,j}b_{j}c_{i}<a_{i}d_{j}\right)\land \left(\bigwedge _{i,k}b_{k}c_{i}<a_{i}d_{k}\right)}