theorem Th10:
  for X being ComplexHilbertSpace, seq being sequence of X
  holds seq is summable iff for r st r > 0 ex k
st for n, m st n >= k & m >= k holds ||.(Partial_Sums(seq)).n - (Partial_Sums(
  seq)).m.|| < r
by CLVECT_2:65,CLVECT_2:58,CLVECT_2:def 11;
