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

theorem Th7:
  x <= 0 implies |.x.| = -x
proof
  assume
A1: x <= 0;
  per cases by A1;
  suppose
    x < 0;
    hence thesis by Def1;
  end;
  suppose
A2: x = 0;
    then -0 = -x;
    hence thesis by A2,Def1;
  end;
end;
