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At: finite-partition 1

  k:c:(0k).
  p:(k( List)). 
  sum(||p(j)|| | j < k) = 0
  & (j:kx,y:||p(j)||. x<y  (p(j))[x]>(p(j))[y])
  & (j:kx:||p(j)||. (p(j))[x]<0 & c((p(j))[x]) = j)


By: Auto THEN InstConcl [j.nil] THEN Reduce 0
THEN
Try (RWO Thm* n:a:. sum(a | x < n) = an 0)


Generated subgoal:

1 1. k : 
2. 0k
3. p : k( List)
4. j : k
5. x : ||p(j)||
6. (p(j))[x]<0
  p(j 0 List

1 step

About:
listnilintnatural_numbermultiplyless_thanlambdaapply
functionequalmemberimpliesandall
exists
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