Existence of a Model of $o(\kappa )={\kappa }^{++}$ from Failure of GCH at a Measurable Cardinal

It is well-known that the consistency strength of the GCH failing at a measurable cardinal is the existence of a cardinal $\kappa$ with $o(\kappa )={\kappa }^{++}$. As the literature does not contain more than a proof sketch of the lower bound of this equiconsistency, we give an expository proof which fills in the details in order to fill this gap in the literature.