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

theorem Th9:
   x infinitely< y implies x < y
proof
  assume x infinitely< y;
  then x*1_No < y by SURREALN:48;
  hence thesis;
end;
