reserve
  A,B,X for set,
  S for SigmaField of X;
reserve C for C_Measure of X;

theorem Th6:
  for W,Z being Subset of X holds W in sigma_Field(C) & Z misses W
  implies C.(W \/ Z) = C.W + C.Z
proof
  let W,Z be Subset of X;
  assume that
A1: W in sigma_Field(C) and
A2: Z misses W;
  Z \ W c= X \ W by XBOOLE_1:33;
  then Z c= X \ W by A2,XBOOLE_1:83;
  hence thesis by A1,Th5;
end;
