 When the \(\XL\) logic also comes with a deductive calculus, we can try to use the machinery of correspondence to prove, if possible, Soundness and Completeness for \(\XL\). In order to prove these theorems, one needs to prove a Theorem of deductive correspondence between the \(\XL\) calculus and the many-sorted one, modulo \(\Delta\). So, the next goal is to prove: