graph
1
2
Sections
Graphs
Doc
Rank
Theorem
Name
4
Thm*
n,m:
, f:(
n
m). Inj(
n;
m; f)
n
m
[pigeon-hole]
cites
3
Thm*
n,k:
, c:(
n
k).
p:(
k
(
List)). sum(||p(j)|| | j < k) = n & (
j:
k, x,y:
||p(j)||. x < y
(p(j))[x] > (p(j))[y]) & (
j:
k, x:
||p(j)||. (p(j))[x] < n & c((p(j))[x]) = j)
[finite-partition]
0
Thm*
k,b:
, f:(
k
). (
x:
k. f(x)
b)
sum(f(x) | x < k)
b
k
[sum_bound]
graph
1
2
Sections
Graphs
Doc