Embedding In in a 2-generator inverse subsemigroup of In+2

Given an integer n, we show that L-n embeds in a 2-generated subsemigroup of Ln+2, which is an inverse semigroup. An immediate consequence of this result is the following, which is analogous to the case for groups and semigroups: every finite inverse semigroup may be embedded in a finite 2-generated semigroup which is an inverse semigroup.