graph 1 1 Sections Graphs Doc

Def sum(f(x) | x < k) == primrec(k;0;x,n. n+f(x))

is mentioned by

Thm* n:, a,b:. sum(a+bi | i < n) = ((n(a+a+b(n-1))) 2)[sum_arith]
Thm* n:, a,b:. sum(a+bi | i < n)2 = n(a+a+b(n-1))[sum_arith1]
Thm* k:, f,g:(k), p:(k). sum(if p(i) f(i)+g(i) else f(i) fi | i < k) = sum(f(i) | i < k)+sum(if p(i) g(i) else 0 fi | i < k)[sum-ite]
Thm* k,b:, f:(k). (x:k. bf(x)) bksum(f(x) | x < k)[sum_lower_bound]
Thm* k,b:, f:(k). (x:k. f(x)b) sum(f(x) | x < k)bk[sum_bound]
Thm* k:, f,g:(k). (x:k. f(x)g(x)) sum(f(x) | x < k)sum(g(x) | x < k)[sum_le]

In prior sections: mb nat mb list 2

Try larger context: Graphs

graph 1 1 Sections Graphs Doc