 reserve a for non empty set;
 reserve b, x, o for object;
reserve R for right_zeroed add-associative right_complementable Abelian
  well-unital distributive associative non trivial non trivial doubleLoopStr;

theorem
    for f be Polynomial of 0,R holds dom f = Bags 0 & Bags 0 = {{}}
    & rng f = {f.(EmptyBag 0)}
    proof
      let f be Polynomial of 0,R;
      dom f = Bags 0 by FUNCT_2:def 1;
      hence thesis by Th15,FUNCT_1:4;
    end;
