 reserve o,o1,o2 for object;
 reserve n for Ordinal;
 reserve R,L for non degenerated comRing;
 reserve b for bag of 1;

theorem Th13:
   for b be bag of 1 holds
   rng(divisors b) = {x where x is bag of 1 : x.0 <= b.0}
   proof
     let b be bag of 1;
A1:  for o holds o in {x where x is bag of 1 : x.0 <= b.0} implies
     o in rng(divisors b)
     proof
       let o;
       assume o in {x where x is bag of 1 : x.0 <= b.0}; then
       consider x1 be bag of 1 such that
A2:    o = x1 & x1.0 <= b.0;
       thus thesis by A2, Th12;
     end;
     for o holds o in rng divisors b implies
     o in {x where x is bag of 1 : x.0 <= b.0}
     proof
       let o;
       assume
A3:    o in rng(divisors b); then
       reconsider x1 = o as bag of 1;
       x1.0 <= b.0 by A3,Th12;
       hence thesis;
     end;
     hence thesis by A1,TARSKI:2;
   end;
