We can use induction also to show that the G-S algorithm outputs the (unique) employer-optimal stable matching in which every employer e is matched with best (e). 1. Prove the following claim. Claim: At the end of every iteration k of the While loop, every employer e has only considered applicants that it ranks at least as high as best(e). Moreover, if e has considered best(e) on or before iteration k, then e is matched with best(e) at the end of iteration k