Nuprl - Proof: Ramsey-recursion 1 1 1

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At: Ramsey-recursion 1 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: (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])

By: RWO Thm* as,bs:T List. ||as @ bs|| = ||as||+||bs|| 0 THEN Reduce 0

Generated subgoal:

1 13. ||s|| = k-1
14. x,y:||s||. x < y s[x] < s[y]
15. x: (||s||+1)
16. y: (||s||+1)
17. x < y
(s @ [(n-1)])[x] < (s @ [(n-1)])[y] 4 steps

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