(10steps total)
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At:
pigeon-hole
n,m:
, f:(
n
m). Inj(
n;
m; f)
n
m
By:
Auto
THEN
Inst
Thm*
finite-partition [n;m;f]
THEN
ExRepD
Generated subgoal:
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
n
m
9
steps
About:
(10steps total)
PrintForm
Definitions
Lemmas
graph
1
2
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Graphs
Doc