Nuprl - Proof: finite-partition 2 2 2 1

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

At: finite-partition 2 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
9. j: k
10. x:||p(j)||. (p(j))[x] < n-1 & c((p(j))[x]) = j
11. c(n-1) = j

x@0:||[(n-1) / (p(j))]||. [(n-1) / (p(j))][x@0] < n & c([(n-1) / (p(j))][x@0]) = j

By: Reduce 0 THEN Analyze 0 THEN CaseNat 0 `x@0' THEN Reduce 0

Generated subgoals:

1 12. x@0: (||p(j)||+1)
13. x@0 = 0
n-1 < n & c(n-1) = j Auto

2 12. x@0: (||p(j)||+1)
13. x@0 = 0
[(n-1) / (p(j))][x@0] < n & c([(n-1) / (p(j))][x@0]) = j 5 steps

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