(41steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

At: Ramsey 2

1. k:
2. 0 < k
3. 0 < k-1 (L: List. 0 < ||L|| (r:. r- > L^k-1))
4. k = 1
5. 0 < k
6. L: List
7. 0 < ||L||
r:. r- > L^k

By:
((RepeatFor 2 (MoveToConcl -1)) THEN (InductionOn (d = sum(L[i] | i < ||L||)) CompNatInd)) THENA ((Try (Fold `member` 0)) THEN Analyze THEN (BackThru Thm* n:, f:(n). (x:n. 0f(x)) 0sum(f(x) | x < n)))
THEN
Try (BackThru Thm* n:, f:(n). (x:n. 0f(x)) 0sum(f(x) | x < n))


Generated subgoal:

16. d:
7. d1:. d1 < d (L: List. sum(L[i] | i < ||L||) = d1 0 < ||L|| (r:. r- > L^k))
8. L: List
9. sum(L[i] | i < ||L||) = d
10. 0 < ||L||
r:. r- > L^k
34 steps

About:
listintnatural_numbersubtractless_thanfunctionequalimpliesallexists

(41steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc