reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  M for sigma_Measure of S,
  f,g for PartFunc of X,COMPLEX,
  r for Real,
  c for Complex,
  E,A,B for Element of S;

theorem Th6:
  Re(f-g) = Re f - Re g & Im(f-g) = Im f - Im g
proof
  Re(f-g) = Re f + Re -g by Th5;
  then
A1: Re(f-g) = Re f + (-1)(#)(Re g) by Th2;
  Im(f-g) = Im f + Im -g by Th5;
  hence thesis by A1,Th2;
end;
