... ing the degree of a cut to be the sum of sizes of the proofs of its two premises, where the size is the num- ber of nodes in the proof. 3 2.2 Difficulties in deciding L(/,\,v)}-T ::¢, x So the ... r. Then one defines two things: a degree of the Cut leading to r, and a transformation taking the proof of r to an alternative proof of r, such that either the trans- formed proof of ... proof of a sequent with a 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...