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

theorem Th67:
   r <> 0 implies not uReal.r * No_omega^ y == 0_No
proof
  assume r<>0;
  then |. uReal.r * No_omega^ y .|, No_omega^ y are_commensurate by Th66;
  then |. uReal.r * No_omega^ y .| is positive by Th3;
  hence thesis by Def6;
end;
