
theorem
  for I being non empty set,
      G being Abelian TopaddGroup,
      s being (the carrier of G)-valued ManySortedSet of I,
      x being Point of G,
      B being basis of BOOL2F NeighborhoodSystem x holds
  x in lim_f Partial_Sums(s)
    iff
  for b being Element of B ex i being Element of OrderedFIN I st
  for j being Element of OrderedFIN I st i <= j holds (Partial_Sums(s)).j in b
  by Th12;
