# $X$ is a point in a bounded polyhedron $\ \in R^n$ with $n-1$ active constraints

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?