 reserve A,B,O for Ordinal,
      n,m for Nat,
      a,b,o for object,
      x,y,z for Surreal,
      X,Y,Z for set,
      Inv,I1,I2 for Function;

theorem
  Inv is Y -surreal-valued & X c= Y implies
    Inv is X -surreal-valued;
