reserve A,B for Ordinal,
        o for object,
        x,y,z for Surreal,
        n for Nat,
        r,r1,r2 for Real;

theorem Th31:
   0_No <= |.x.|
proof
  per cases;
  suppose 0_No <= x;
    hence thesis by Def6;
  end;
  suppose
A1: x < 0_No;
    then 0_No = -0_No < -x by SURREALR:10;
    hence thesis by Def6,A1;
  end;
end;
