Nuprl - Proof: Ramsey 2 1 2 2 2 1 2 3 1 1 2

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At: Ramsey 2 1 2 2 2 1 2 3 1 1 2

1. k:
2. 0 < k
3. 0 < k-1 (L: List. 0 < ||L|| (r:. r- > L^k-1))
4. k = 1
5. 0 < k
6. d:
7. d1:. d1 < d (L: List. sum(L[i] | i < ||L||) = d1 0 < ||L|| (r:. r- > L^k))
8. L: List
9. sum(L[i] | i < ||L||) = d
10. 0 < ||L||
11. (i:||L||. L[i] < k)
12. i:||L||. 2L[i]
13. L: List. sum(L[i] | i < ||L||) = d-1 0 < ||L|| (r:. r- > L^k)
14. i: ||L||
15. d:. sum(L[x]-L[i--][x] | x < ||L||) = d sum(L[x] | x < ||L||) = sum(L[i--][x] | x < ||L||)+d
16. sum(L[x]-L[i--][x] | x < ||L||) = L[i]-L[i--][i]

sum(L[x]-L[i--][x] | x < ||L||) = 1

By: HypSubst' -1 0

Generated subgoal:

1 L[i]-L[i--][i] = 1 1 step

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(41steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc