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 Th12:
  X (+) Y = Y (+) X
proof
  thus X (+) Y c= Y (+) X
  proof
    let p be object;
    assume p in X (+) Y; then
    ex p1,p2 being Point of T st p = p1+p2 & p1 in X & p2 in Y;
    hence thesis;
  end;
  let p be object;
  assume p in Y (+) X;
  then ex p1,p2 being Point of T st p = p1+p2 & p1 in Y & p2 in X;
  hence thesis;
end;
