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

theorem Th15:
  x - 0 = x
proof
  per cases by XXREAL_0:14;
  suppose
    x in REAL;
    then reconsider a = x as Real;
    x - 0 = a - 0 .= x;
    hence thesis;
  end;
  suppose
    x = -infty;
    hence thesis by Th14;
  end;
  suppose
    x = +infty;
    hence thesis by Th13;
  end;
end;
