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

At: Ramsey-base-case 1 1 1 2 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. 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
9. (c:||L||. L[c]||p(c)||)
sum(||p(j)|| | j < ||L||)sum(L[i]-1 | i < ||L||)

By: BackThru Thm* k:, f,g:(k). (x:k. f(x)g(x)) sum(f(x) | x < k)sum(g(x) | x < k)

Generated subgoal:

110. i: ||L||
||p(i)||L[i]-1
3 steps

About:
listconsnilintnatural_numberaddsubtractless_thanset
lambdaapplyfunctionequalimpliesandall
exists

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