reserve x, y, z, s for ExtReal;
reserve i, j for Integer;
reserve n, m for Nat;

theorem Th1:
  x = -x implies x = 0
  proof
    per cases by XXREAL_0:14;
    suppose x = +infty or x = -infty;
      hence thesis;
    end;
    suppose x in REAL;
      then reconsider y = x as Element of REAL;
      -x = -y by XXREAL_3:def 3;
      hence thesis;
    end;
  end;
