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

At: Ramsey 2 1 2 2 2 2 2 1 1
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||. r:. r- > L[i--]^k
15. R: List
16. ||R|| = ||L||
17. i:||L||. 0 < L[i] R[i]- > L[i--]^k
18. r:
19. r- > R^k-1
20. r+1- > L^k
r:. r- > L^k
By: InstConcl [r+1]
Generated subgoals:

None

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listintnatural_numberaddsubtractless_thanequalimpliesallexists

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