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

At: Ramsey-base-case 1 1 1 1 1 1 1

1. L: List
2. n:
3. G: {s:(n List)| ||s|| = 1 & (x,y:||s||. x < y s[x] < s[y]) }||L||
4. c: ||L||
5. A: List
6. m:
7. m||A||
8. x:||A||. A[x] < n & G([A[x]]) = c
9. x,y:||A||. x < y A[x] > A[y]
f:(mn). increasing(f;m) & (s:m. G([(f(s))]) = c)

By:
InstConcl [x.A[(||A||-(x+1))]]
THEN
Try (Complete Auto)


Generated subgoals:

1 (x.A[(||A||-(x+1))]) mn2 steps
 
2 increasing(x.A[(||A||-(x+1))];m) & (s:m. G([((x.A[(||A||-(x+1))])(s))]) = c)3 steps
 
310. f: mn
(increasing(f;m) & (s:m. G([(f(s))]) = c)) Prop
1 step

About:
listconsnilintnatural_numberaddsubtractless_thansetlambda
applyfunctionequalmemberpropimpliesandallexists

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