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

theorem
  sigma_Meas(C) is complete
proof
  let A be Subset of X;
  let B;
  assume that
A1: B in sigma_Field(C) and
A2: A c= B and
A3: (sigma_Meas(C)).B = 0.;
  reconsider B as Subset of X by A1;
  C is nonnegative by Def1;
  then
A4: 0.<= C.A by MEASURE1:def 2;
  C.B = 0. by A1,A3,Def3;
  then C.A = 0. by A2,A4,Def1;
  hence thesis by Th15;
end;
