
theorem
  for n being Ordinal, T being admissible TermOrder of n, b1,b2 being
  bag of n holds b1 divides b2 implies b1 <= b2,T
proof
  let n be Ordinal, T be admissible TermOrder of n, b1,b2 be bag of n;
  assume b1 divides b2;
  then consider b3 being bag of n such that
A1: b2 = b1 + b3 by Th1;
  EmptyBag n <= b3,T by Th9;
  then [EmptyBag n,b3] in T;
  then [EmptyBag n + b1,b2] in T by A1,BAGORDER:def 5;
  then [b1,b2] in T by PRE_POLY:53;
  hence thesis;
end;
