n:, f:({0..n}), m:{0..(n+1)}.
sum(f(x) | x < n) = sum(f(x) | x < m)+sum(f(x+m) | x < n - m) 

latex

Definitions	False, A, A  B, i  j , P  Q, tt, (i = j), if b then t else f fi , Y, primrec(n;b;c), t  T, sum(f(x) | x < k), x:A. B(x), , {T}, SQType(T), P & Q, i  j < k, suptype(S; T), S  T, {i..j}, ff, x. t(x), , x(s), P  Q, Dec(P), P  Q, Unit, ,
Lemmas	ge wf, nat properties, nat wf, int seg wf, decidable int equal, le wf, not functionality wrt iff, assert of bnot, eqff to assert, assert of eq int, eqtt to assert, iff transitivity, not wf, bnot wf, sum wf, assert wf, bool wf, eq int wf, ifthenelse wf