How do I "apply" a loop invariant?
You “state” a loop invariant - that’s an educated guess. 

You “prove” a loop invariant - you show it’s true before the loop is first entered, and you show that if it’s true before an iteration, then it is true after the iteration. 

You apply the loop invariant - you take the fact that the loop invariant is proven, and the fact that the loop stopped iterating, to prove facts that hold after the loop is finished.