
theorem bag1:
for Z being non empty set
for B1,B2 being bag of Z st B1 divides B2 holds card B1 <= card B2
proof
let Z be non empty set, B1,B2 be bag of Z;
assume B1 divides B2;
then consider B3 being bag of Z such that A: B2 = B1 + B3 by bag1a;
card B2 = card B1 + card B3 by A,UPROOTS:15;
hence thesis by NAT_1:11;
end;
