(99steps total)
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Ramsey-recursion
1
2
1
1
1
1.
r:
2.
k:
3.
L:
List
4.
R:
List
5.
2
k
6.
||R|| = ||L||
7.
i:
||L||. 0 < L[i]
R[i]- > L[i--]^k
8.
r- > R^k-1
9.
n:
10.
r+1
n
11.
G:
{s:(
n List)| ||s|| = k
& (
x,y:
||s||. x < y
s[x] < s[y]) }
||L||
12.
c:
||R||
13.
f:
R[c]
(n-1)
14.
increasing(f;R[c])
15.
s:
R[c] List. ||s|| = k-1
(
x,y:
||s||. x < y
s[x] < s[y])
G(map(f;s) @ [(n-1)]) = c
16.
0 < L[c]
17.
R[c]- > L[c--]^k
18.
G:({s:(
R[c] List)| ||s|| = k
& (
x,y:
||s||. x < y
s[x] < s[y]) }
||L[c--]||).
c@0:
||L[c--]||, f:(
L[c--][c@0]
R[c]). increasing(f;L[c--][c@0]) & (
s:
L[c--][c@0] List. ||s|| = k
(
x,y:
||s||. x < y
s[x] < s[y])
G(map(f;s)) = c@0)
(
s. G(map(f;s)))
{s:(
R[c] List)| ||s|| = k
& (
x,y:
||s||. x < y
s[x] < s[y]) }
||L[c--]||
By:
Analyze
THEN
Analyze -1
THEN
Analyze -1
THEN
Subst' (||L[c--]|| = ||L||) 0
THEN
Try (RWO
Thm*
L:
List, i:
||L||. 0 < L[i]
||L[i--]|| = ||L||
0)
Generated subgoal:
1
19.
s:
R[c] List
20.
||s|| = k
21.
x,y:
||s||. x < y
s[x] < s[y]
G(map(f;s))
||L||
1
step
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(99steps total)
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