Say I have a set S w/ an associative binary operation *: S x S -> S and a two-sided identity e, and let . Let L and R be elements of S such that L * s = e = s * R
How can I prove that L = R ?
Since the left and right identity are equal to e which is a two-sided identity, that proves that the left and right are equal just by the definition of a two-sided identity right? Is there some more in-depth proof I'm not seeing here?