Introduction to Cut Elimination

Iowa Type Theory Commute

We saw in the last few episodes that proofs in natural deduction can be simplified by removing detours, which occur when an introduction inference is immediately followed by an elimination inference on the introduced formula. What corresponds to this for sequent calculus proofs? The answer is cut elimination. This episode describes the cut rule and what is meant by a cut-elimination procedure. We will talk more about such a procedure in the next episode.