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At: finite-partition 1

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

11. k:
2. c: 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

(26steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc