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

theorem Th11:
  -y < x & x < y implies 0 < y & |.x.| < y
proof
  assume that
A1: -y < x and
A2: x < y;
  per cases;
  suppose
    0 <= x;
    hence thesis by A2,Def1;
  end;
  suppose
A3: not 0 <= x;
    -x < y by A1,XXREAL_3:60;
    hence thesis by A3,Def1;
  end;
end;
