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=== Proof of "ax by bz" (except in case xyxzxyx) ===
=== Proof of "ax by bz" (except in case xyxzxyx) ===
Assume len(S) >= 8. Write S in x's and q's, as above. By PWF, we have that the word of x's and q's is a MOS.
'''Assuming the alternating generator property''', we have two chains of generator g0 (going right). The two cases are:
'''Assuming the alternating generator property''', we have two chains of generator g0 (going right). The two cases are:
  O-O-...-O (m notes)
  O-O-...-O (m notes)
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