Nuprl - Proof: Ramsey-base-case 1 2 2

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At: Ramsey-base-case 1 2 2

1. L: List
2. n:
3. sum(L[i]-1 | i < ||L||)+1n
4. G: {s:(n List)| ||s|| = 1 & (x,y:||s||. x < y s[x] < s[y]) }||L||
5. c: ||L||
6. f:(L[c]n). increasing(f;L[c]) & (s:L[c]. G([(f(s))]) = c)
7. c1: ||L||
8. f: L[c1]n
9. increasing(f;L[c1])
10. s: L[c1] List
11. ||s|| = 1
12. x,y:||s||. x < y s[x] < s[y]

map(f;s) {s:(n List)| ||s|| = 1 & (x,y:||s||. x < y s[x] < s[y]) }

By: Analyze THEN Try (Complete Auto) THEN Analyze -3 THEN All Reduce THEN Try (Complete Auto)

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(30steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc