There Is a Mismatch between Meta and Object Level in Many Calculi

There is a mismatch between meta and object levels in many calculi, like the sequent calculus and natural deduction. The mismatch has undesirable proof theoretical consequences, the most important being the inability to design deductive systems. Since the object level is untouchable (it's the language you want to deal with), one can fix the problem by `improving ́ the meta level; or one can also sort of merge object and meta level by using deep inference.