
theorem
  for f be XFinSequence of COMPLEX, g be FinSequence of COMPLEX holds
    Sum (f^g) = Sum f + Sum g & Sum (g^f) = Sum g + Sum f
  proof
    let f be XFinSequence of COMPLEX, g be FinSequence of COMPLEX;
    A1: Sum (f^g) = Sum (f^(XFS2FS(FS2XFS g)))
    .= Sum (f^(FS2XFS g)) by XFX
    .= Sum f + Sum (FS2XFS g) by AFINSQ_2:55
    .= Sum f + Sum g by FSS;
    Sum (g^f) = Sum (g^(FS2XFS(XFS2FS f)))
    .= Sum (g^(XFS2FS f)) by FXF
    .= Sum g + Sum (XFS2FS f) by RVSUM_2:32
    .= Sum g + Sum f by XSS;
    hence thesis by A1;
  end;
