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
  X (+) {0.T} = X
proof
  thus X (+) {0.T} c= X
  proof
    let x be object;
    assume x in X (+) {0.T};
    then consider y,z being Point of T such that
A1: x=y+z & y in X and
A2: z in {0.T};
    {z} c= {0.T} by A2,ZFMISC_1:31;
    then z = 0.T by ZFMISC_1:18;
    hence thesis by A1;
  end;
  let x be object;
  assume
A3: x in X;
  then reconsider x as Point of T;
  0.T in {0.T} by TARSKI:def 1;
  then
  x+0.T in {y+z where y,z is Point of T : y in X & z in {0.T}} by A3;
  hence thesis;
end;
