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

theorem
  (x <= -y implies y <= -x) & (-x <= y implies -y <= x)
proof
  x <= -y implies --y <= -x by Th38;
  hence x <= -y implies y <= -x;
  -x <= y implies -y <= --x by Th38;
  hence thesis;
end;
