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