... and with either the same path or with path p. Also, in leaves of a proof in L (/'\'v), categories only occur with zero path. Therefore, if we have 124 a proof of a sequent with ... positive occurrence of ViX.X/X and with non-zero path, then there must occur higher in the proof, a sequent with V,.X.X/X occurring again positively and this time with with zero-path. In other words ... leaf such as T ==~ X. One can hy- pothesis X = Y/Z, extend the deduction tree by the rewrite associated with a slash Right rule, obtain- ing once again a leaf with a succedent occurrence of an...