reserve n for Nat;

theorem bag1a:
for X being non empty set,
    b being bag of X holds card b = 0 iff support b = {}
proof
let X be non empty set, b be bag of X;
A: now assume support b = {};
   then b = EmptyBag X by PRE_POLY:81;
   hence card b = 0 by UPROOTS:11;
   end;
now assume card b = 0;
  then b = EmptyBag X by UPROOTS:12;
  hence support b = {};
  end;
hence thesis by A;
end;
