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

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

At: Ramsey-recursion 1 2 1 1 2 1 1 1 1 3 2

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. c: ||R||
13. f: R[c](n-1)
14. increasing(f;R[c])
15. s:R[c] List. ||s|| = k-1 (x,y:||s||. x < y s[x] < s[y]) G(map(f;s) @ [(n-1)]) = c
16. 0 < L[c]
17. R[c]- > L[c--]^k
18. (s. G(map(f;s))) {s:(R[c] List)| ||s|| = k & (x,y:||s||. x < y s[x] < s[y]) }||L[c--]||
19. c@0: ||L[c--]||
20. f@0: (L[c]-1)R[c]
21. increasing(f@0;L[c]-1)
22. s:(L[c]-1) List. ||s|| = k (x,y:||s||. x < y s[x] < s[y]) G(map(f;map(f@0;s))) = c

increasing(f o f@0[L[c]-1:=n-1];L[c]) & (s:L[c] List. ||s|| = k (x,y:||s||. x < y s[x] < s[y]) G(map(f o f@0[L[c]-1:=n-1];s)) = c)

By: Analyze 0

Generated subgoals:

1 increasing(f o f@0[L[c]-1:=n-1];L[c]) 2 steps

2 23. increasing(f o f@0[L[c]-1:=n-1];L[c])
s:L[c] List. ||s|| = k (x,y:||s||. x < y s[x] < s[y]) G(map(f o f@0[L[c]-1:=n-1];s)) = c 47 steps

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

1	`increasing(f o f@0[L[c]-1:=n-1];L[c])`	2 steps

2	23. `increasing(f o f@0[L[c]-1:=n-1];L[c])` `s:L[c] List. \|\|s\|\| = k (x,y:\|\|s\|\|. x < y s[x] < s[y]) G(map(f o f@0[L[c]-1:=n-1];s)) = c`	47 steps