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

At: Ramsey-base-case 1 1 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. 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)||
c:||L||, f:(L[c]n). increasing(f;L[c]) & (s:L[c]. G([(f(s))]) = c)
By: ParallelOp -1
Generated subgoals:

19. c: ||L||
10. L[c]||p(c)||
f:(L[c]n). increasing(f;L[c]) & (s:L[c]. G([(f(s))]) = c)		11 steps
 
29. c: ||L||
10. L[c]||p(c)||
11. c1: ||L||
12. f: L[c1]n
13. increasing(f;L[c1])
14. s: L[c1]
[(f(s))] {s:(n List)| ||s|| = 1 & (x,y:||s||. x < y s[x] < s[y]) }		1 step

About:
listconsnilintnatural_numberaddsubtractless_thansetlambda
applyfunctionequalmemberimpliesandallexists

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