Theorem | Name |
Thm* n: , f:( n  ), i: (n-1). sum(f((i, i+1)(x)) | x < n) = sum(f(x) | x < n) | [sum_switch] |
cites the following: |
Thm* k: , i,j: k. (i, j) k  k | [flip_wf] |
Thm* n: , f:( n  ), m: (n+1).
Thm* sum(f(x) | x < n) = sum(f(x) | x < m)+sum(f(x+m) | x < n-m) | [sum_split] |
Thm* n: , f,g:( n  ).
Thm* ( i: n. f(i) = g(i))  sum(f(x) | x < n) = sum(g(x) | x < n) | [sum_functionality] |