Nuprl - Proof: Ramsey-recursion 1 1

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At: Ramsey-recursion 1 1

1. r:
2. k:
3. L: List
4. R: List
5. 2k
6. ||R|| = ||L||
7. i:||L||. 0 < L[i] R[i]- > L[i--]^k
8. r- > R^k-1
9. n:
10. r+1n
11. G: {s:(n List)| ||s|| = k & (x,y:||s||. x < y s[x] < s[y]) }||L||
12. s: {s:((n-1) List)| ||s|| = k-1 & (x,y:||s||. x < y s[x] < s[y]) }

(s @ [(n-1)]) {s:(n List)| ||s|| = k & (x,y:||s||. x < y s[x] < s[y]) }

By: Analyze -1 THEN Analyze THEN Try (Complete Auto)

Generated subgoal:

1 12. s: (n-1) List
13. ||s|| = k-1 & (x,y:||s||. x < y s[x] < s[y])
||s @ [(n-1)]|| = k & (x,y:||s @ [(n-1)]||. x < y (s @ [(n-1)])[x] < (s @ [(n-1)])[y]) 5 steps

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(99steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc