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

theorem Th9:
  A in sigma_Field(C) & B in sigma_Field(C) implies A /\ B in sigma_Field(C)
proof
  assume that
A1: A in sigma_Field(C) and
A2: B in sigma_Field(C);
A3: X \ B in sigma_Field(C) by A2,Th7;
  A /\ B c= X /\ X by A1,A2,XBOOLE_1:27;
  then
A4: A /\ B = X /\ (A /\ B) by XBOOLE_1:28
    .= X \ (X \(A /\ B)) by XBOOLE_1:48
    .= X \ ((X \ A) \/ (X \ B)) by XBOOLE_1:54;
  X \ A in sigma_Field(C) by A1,Th7;
  then (X \ A) \/ (X \ B) in sigma_Field(C) by A3,Th8;
  hence thesis by A4,Th7;
end;
