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 ex y being Point of T st x=y & {0.T}+y c= X;
    then {x} c= X by Th2;
    hence thesis by ZFMISC_1:31;
  end;
  let x be object;
  assume
A1: x in X;
  then reconsider xx=x as Point of T;
  {x} c= X by A1,ZFMISC_1:31;
  then {0.T}+xx c= X by Th2;
  hence thesis;
end;
