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 Th42:
  X (O) X = X
proof
  thus X (O) X c= X by Th41;
  let x be object;
  assume
A1: x in X;
  then reconsider x1=x as Point of T;
  X+0.T c= X by Th21;
  then 0.T in X (-) X;
  then x1+0.T in (X (-) X) (+) X by A1;
  hence thesis;
end;
