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

theorem Th64:
  not x==0_No & y == 0_No implies y infinitely< |.x.|
proof
  assume
A1: not x==0_No & y == 0_No;
  then
A2: |.x.| is positive by Th36;
  let r be positive Real;
  uReal.r * y == uReal.r * 0_No = 0_No by A1,SURREALR:51;
  hence thesis by SURREALO:4,A2;
end;
