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 Th4:
  for X st X = {} holds X+x = {}
proof
  let X;
  assume
A1: X = {};
  now
    given y being object such that
A2: y in X+x;
    ex y1 being Point of T st y = y1+x & y1 in X by A2;
    hence contradiction by A1;
  end;
  hence thesis by XBOOLE_0:def 1;
end;
