reserve T for non empty Abelian
  add-associative right_zeroed right_complementable RLSStruct,
  X,Y,Z,B,C,B1,B2 for Subset of T,
  x,y,p for Point of T;

theorem
  (B (-) X)\/(B (-) Y) c= B (-) (X/\Y)
proof
  let x be object;
  assume x in (B (-) X)\/(B (-) Y);
  then x in B (-) X or x in B (-) Y by XBOOLE_0:def 3;
  then consider y being Point of T such that
A1: x=y & X+y c= B or x=y & Y+y c= B;
  (X+y)/\(Y+y) c= B
  proof
    let a be object;
    assume
A2: a in (X+y)/\(Y+y);
    then
A3: a in X+y by XBOOLE_0:def 4;
A4: a in Y+y by A2,XBOOLE_0:def 4;
    per cases by A1;
    suppose
      X+y c= B;
      hence thesis by A3;
    end;
    suppose
      Y+y c= B;
      hence thesis by A4;
    end;
  end;
  then (X/\Y)+y c= B by Th28;
  hence thesis by A1;
end;
