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

At: Ramsey 2 1 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. f: i:||L||r:r- > L[i--]^k
R: List. ||R|| = ||L|| & (i:||L||. 0 < L[i] R[i]- > L[i--]^k)

By: InstConcl [mklist(||L||;i.1of(f(i)))]

Generated subgoals:

1 mklist(||L||;i.1of(f(i))) List1 step
 
2 ||mklist(||L||;i.1of(f(i)))|| = ||L|| & (i:||L||. 0 < L[i] mklist(||L||;i.1of(f(i)))[i]- > L[i--]^k)4 steps
 
315. R: List
(||R|| = ||L|| & (i:||L||. 0 < L[i] R[i]- > L[i--]^k)) Prop
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(41steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc