Rank | Theorem | Name |
2 | Thm* P:(T  ), a:array(T), i: |a|, v:T. array-count(v.P(v);a[i:=v]) = array-count(v.P(v);a)+if P(v) if P(a[i]) 0 else 1 fi ;P(a[i]) -1 else 0 fi | [array-count-update] |
cites |
1 | Thm* n: , f:( n  ), m: n. sum(f(x) | x < n) = f(m)+sum(if x= m 0 else f(x) fi | x < n) | [isolate_summand] |
0 | Thm* a:array(T), j,i: |a|, v:T. a[i:=v][j] ~ if j= i v else a[j] fi | [array-update-select] |
0 | Thm* n: , f,g:( n  ). ( i: n. f(i) = g(i))  sum(f(x) | x < n) = sum(g(x) | x < n) | [sum_functionality] |