reserve x,y,z,w for ExtReal,
  r for Real;

theorem Th4:
  x + 0 = x
proof
  per cases by XXREAL_0:14;
  suppose
    x in REAL;
    then reconsider r=x as Real;
    r + 0 = r;
    hence thesis;
  end;
  suppose
    x = -infty or x = +infty;
    hence thesis by Def2;
  end;
end;
