I am having troubles in understanding the proof of the following proposition.
Proposition If $f(x)$ is a convex function and $x^*$ is a solution to VI($\nabla f$,$K$), then $x^*$ is a solution to the optimization problem
$$\min f(x), \text{ subject to: } x \in K.$$
Where VI=Variational Inequality problem and $K$ is a convex set.
Proof Since $f(x)$ is convex, $$f(x)\geq f(x^*)+\langle \nabla f(x^*)^T,x-x^*\rangle, \quad \forall x \in K.$$
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I do not understand this first step in the proof.