
theorem
  for f be XFinSequence of COMPLEX, g be FinSequence of COMPLEX holds
  XProduct (f^g) = XProduct f * Product g &
  Product (g^f) = Product g * XProduct f
  proof
    let f be XFinSequence of COMPLEX, g be FinSequence of COMPLEX;
    A1: XProduct (f^g) = Product XFS2FS (f^g) by XPF
    .= Product ((XFS2FS f)^g) by SSX
    .= Product (XFS2FS f) * Product g by FAF
    .= XProduct f * Product g by XPF;
    Product (g^f) = Product (g^(FS2XFS(XFS2FS f)))
    .= Product (g^(XFS2FS f)) by FXF
    .= Product g * Product (XFS2FS f) by FAF
    .= Product g * XProduct f by XPF;
    hence thesis by A1;
  end;
