 When the \(\XL\) logic under scrutiny has a concept of logical consequence, we may try to prove the Main theorem; that is, that consequence in \(\XL\) (\(\Pi \models _{\Str(\XL)}\varphi\)) is equivalent to consequence of translations in MSL, modulo the theory \(\Delta\). To prove the main theorem, the reverse conversion of structures, \(\Conv_{2}\), should be used. Our goal in defining it is to prove the following: