In response to a question:

I first tried to show that cascade discontinuities are necessary.

Second assume these discontinuities leave behind a split rather than just a 
shift.

The assumption results in an additional contradictory situation giving two 
running contradictions.  Result - splits result in a contradiction 
cascade.  However, a chain of discontinuities consisting of just shifts 
clears all these contradictions including the original one.

Hal


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