suppose we have a polytope $P$ in $R^{4}$ and $-1\leq x_{3}\leq 4$ and $0\leq x_{4}\leq 6$, if I replace the upper and lower bound of $x_{3}$ and $x_{4}$ (it depends on the sign of variables $x_{4}$ and $x_{3}$ to choose upper or lower bound) I will get a polytope $P^{\prime}$ in $R^{2}$ with valid constraints for original polytope $P$. what is relation between this polytope and the original polytope $P$ in $R^{4}$? and if I eliminate $x_{4}$ and $x_{3}$ and so project this polytope to $R^{2}$ what is relation between this polytope and $P^{\prime}$?

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    $\begingroup$ I’m a little confused by what you’re asking. Can you provide a more concrete example? $\endgroup$ – David M. May 5 at 22:16

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