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 Th2:
  {0.T} + x = {x}
proof
  thus {0.T} + x c= {x}
  proof
    let a be object;
    assume a in {0.T} + x;
    then consider q being Point of T such that
A1: a=q+x and
A2: q in {0.T};
    {q} c= {0.T} by A2,ZFMISC_1:31;
    then q = 0.T by ZFMISC_1:18;
    then {a} c= {x} by A1;
    hence thesis by ZFMISC_1:31;
  end;
  let a be object;
  assume a in {x};
  then {a} c= {x} by ZFMISC_1:31;
  then a = x by ZFMISC_1:18;
  then
A3: a = 0.T + x;
  0.T in {0.T} by ZFMISC_1:31;
  hence thesis by A3;
end;
