2. m :
3. f :
n
m
4. p :
nn
5. q :
mm
6. Bij(
n; n; p)
7. Bij(
m; m; q)
sum(sum(f(p(x),q(y)) | y < m) | x < n) = sum(sum(f(x,y) | y < m) | x < n)
nm
nn
mm
n; n; p)
m; m; q)
sum(sum(f(p(x),q(y)) | y < m) | x < n) = sum(sum(f(x,y) | y < m) | x < n)| By: |
Thm*  n:, f:(n), p:(nn).
Thm* Bij( n; n; p)   sum(f(p(x)) | x < n) = sum(f(x) | x < n)
[n;  x.sum(f(x,q(y)) | y < m);p] |
| 1 |
x.sum(f(x,q(y)) | y < m))(p(x)) | x < n)
8. = 8. sum(( x.sum(f(x,q(y)) | y < m))(x) | x < n)
sum(sum(f(p(x),q(y)) | y < m) | x < n) = sum(sum(f(x,y) | y < m) | x < n) | 3 steps |
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