At:
pigeon-hole
1
1
1.
n:
2.
m:
3.
f:
n

m
4.
Inj(
n;
m; f)
5.
p:
m
(
List)
6.
sum(||p(j)|| | j < m) = n
7.
j:
m, x,y:
||p(j)||. x < y 
(p(j))[x] > (p(j))[y]
8.
j:
m, x:
||p(j)||. (p(j))[x] < n & f((p(j))[x]) = j
sum(||p(j)|| | j < m)
1
m
By:
BackThru
Thm*
k,b:
, f:(
k

). (
x:
k. f(x)
b) 
sum(f(x) | x < k)
b
k
Generated subgoal:
1 | 9. j: m ||p(j)|| 1 | 7 steps |
About: