reserve n for Nat;

theorem bbag:
for X being non empty set,
    b being bag of X holds b is zero iff support b = {}
proof
let X being non empty set, b being bag of X;
now assume support b = {};
   then for o be object st o in X holds b.o = {} by PRE_POLY:def 7;
   hence b is zero by PBOOLE:6;
   end;
hence thesis;
end;
