starting pile, which
is not part of the normal intuition, regardless of how it may be 
expressed in vague linguistic terms.

   The formalized statement is false because thus taken out of context 
it is effectively a mathematical equation:
  heap - 1 = heap
  and if "heap" remains unchanged on both sides of the equaiton,
the result is that 1 = 0.

   So, yes, there is something wrong with the formalization,
in that it does not accurately reflect the normal intuition.

    The only formalization that I can t