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

theorem Th7:
  x + -x = 0
proof
  per cases by XXREAL_0:14;
  suppose
    x = -infty;
    hence thesis by Th5;
  end;
  suppose
    x in REAL;
    then reconsider x as Real;
    reconsider y=-x as Real;
    x + y = 0;
    hence thesis;
  end;
  suppose
    x = +infty;
    hence thesis by Th6;
  end;
end;
