Nuprl - Proof: Ramsey-base-case 1 1

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At: Ramsey-base-case 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||

c:||L||, f:(L[c]n). increasing(f;L[c]) & (s:L[c]. G([(f(s))]) = c)

By: (Inst Thm* finite-partition [n;||L||;x.G([x])]) THENA (Auto THEN Analyze THEN (Reduce 0)) THEN ExRepD

Generated subgoal:

1 5. p: ||L||( List)
6. sum(||p(j)|| | j < ||L||) = n
7. j:||L||, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
8. j:||L||, x:||p(j)||. (p(j))[x] < n & (x.G([x]))((p(j))[x]) = j
c:||L||, f:(L[c]n). increasing(f;L[c]) & (s:L[c]. G([(f(s))]) = c) 20 steps

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