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

theorem Th36:
  not x == 0_No implies |.x.| is positive
proof
  assume not x == 0_No;
  then per cases;
  suppose
A1: 0_No < x;
    then 0_No <= x;
    hence thesis by A1,Def6;
  end;
  suppose
A2: x < 0_No;
    then |.x.| = -x by Def6;
    hence thesis by A2,SURREALR:10,23;
  end;
end;
