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

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At: Ramsey-base-case 1 2 1 1

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
7. increasing(f;L[c]) & (s:L[c]. G([(f(s))]) = c)

increasing(f;L[c]) & (s:L[c] List. ||s|| = 1 (x,y:||s||. x < y s[x] < s[y]) G(map(f;s)) = c)

By: Analyze -1 THEN Analyze 0 THEN Try Trivial

Generated subgoal:

1 7. increasing(f;L[c])
8. s:L[c]. G([(f(s))]) = c
9. increasing(f;L[c])
s:L[c] List. ||s|| = 1 (x,y:||s||. x < y s[x] < s[y]) G(map(f;s)) = c 2 steps

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