(\exists x_1)(\exists x_2)\ldots(\exists x_n)\bigwedge_{1\le s\le n_1\atop 1\le t\le n_2}\Bigg[\sum_{j=1}^{n-1}\gamma_{tj} x_j -\delta_t\ge x_n \quad\land\quad x_n\ge \beta_s-\sum_{j=1}^{n-1}\alpha_{sj} x_j\Bigg]\Longleftrightarrow\\(\exists x_1)(\exists x_2)\ldots(\exists x_{n-1})\bigwedge_{1\le s\le n_1\atop 1\le t\le n_2}\Bigg[\sum_{j=1}^{n-1}\gamma_{tj} x_j -\delta_t\ge \beta_s-\sum_{j=1}^{n-1}\alpha_{sj} x_j\Bigg ]\Longleftrightarrow\\(\exists x_1)\ldots(\exists x_n)\Bigg[\min_{1\le t\le n_2}\left (\sum_{j=1}^{n-1}\gamma_{tj} x_j-\delta_t\right)\ge x_n\ge \max_{1\le s\le n_1}\left ( \beta_s-\sum_{j=1}^{n-1}\alpha_{sj} x_j\right )\Bigg]