(41steps total)
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2
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At:
Ramsey
2
1
2
2
2
1
2
3
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.
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||
11.
(
i:
||L||. L[i] < k)
12.
i:
||L||. 2
L[i]
13.
L:
List. sum(L[i] | i < ||L||) = d-1
0 < ||L||
(
r:
. r- > L^k)
14.
i:
||L||
sum(L[i--][i@0] | i@0 < ||L||) = d-1
By:
(Inst
Thm*
n:
, f,g:(
n
), d:
. sum(f(x)-g(x) | x < n) = d
sum(f(x) | x < n) = sum(g(x) | x < n)+d [||L||;
j. L[j];
j. L[i--][j]]) THENA (Auto THEN (AutoInst [i]) THEN (RWO
Thm*
L:
List, i:
||L||. 0 < L[i]
||L[i--]|| = ||L||
0) THEN (AutoInst [i]))
Generated subgoal:
1
15.
d:
. sum(L[x]-L[i--][x] | x < ||L||) = d
sum(L[x] | x < ||L||) = sum(L[i--][x] | x < ||L||)+d
sum(L[i--][i@0] | i@0 < ||L||) = d-1
7
steps
About:
(41steps total)
PrintForm
Definitions
Lemmas
graph
1
2
Sections
Graphs
Doc