 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 Th11:
  Y c= Z implies divset(Y,x,X,Inv) c= divset(Z,x,X,Inv)
proof
  assume
A1: Y c= Z;
  let o;
  assume o in divset(Y,x,X,Inv);
  then ex lamb be object st lamb in Y & o in divs(lamb,x,X,Inv) by Def3;
  hence thesis by A1,Def3;
end;
