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Lets take a vector $d$ which is orthogonal to the active constraint.

Since the polyhedron is bounded:

We'll move to a point $x+\alpha*d$ where we will activate another constraint let's name it j.

We'll move to a point $x-\beta*d$ where we will activate another constraint let's name it k.

$\alpha, \ \beta > 0 $

How can I prove that k and j are different constraints?

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