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

theorem Th43:
  |.x.| infinitely< z & |.y.| infinitely< z implies
     |. x - y .| infinitely< z
proof
  assume
A1: |.x.| infinitely< z & |.y.| infinitely< z;
  then |. - y  .| infinitely< z by Th42;
  hence thesis by Th41,A1;
end;
