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

At: finite-partition 2 2 1
1. n:
2. 0 < n
3. k:
4. c: nk
5. p: k( List)
6. sum(||p(j)|| | j < k) = n-1
7. j:k, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
8. j:k, x:||p(j)||. (p(j))[x] < n-1 & c((p(j))[x]) = j
j:k, x,y:||if c(n-1)=j [(n-1) / (p(j))] else p(j) fi||. x < y if c(n-1)=j [(n-1) / (p(j))] else p(j) fi[x] > if c(n-1)=j [(n-1) / (p(j))] else p(j) fi[y]
By:
ParallelOp -2
THEN
SplitOnConclITE
THEN
Try Trivial
Generated subgoal:

19. j: k
10. x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
11. c(n-1) = j
x@0,y:||[(n-1) / (p(j))]||. x@0 < y [(n-1) / (p(j))][x@0] > [(n-1) / (p(j))][y]		3 steps

About:
listconsifthenelseintnatural_number
subtractless_thanapplyfunctionequalimpliesall

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