reserve n for Nat;

theorem bb7:
for X being non empty set,
    b being non empty bag of X,
    x being Element of X
holds support b = {x} iff (b = ({x},b.x)-bag & b.x <> 0)
proof
let X be non empty set, b be non empty bag of X, x be Element of X;
now assume AS: support b = {x};
  then x in support b by TARSKI:def 1;
  hence b = ({x},b.x)-bag & b.x <> 0 by AS,bb7a,PRE_POLY:def 7;
  end;
hence thesis by UPROOTS:8;
end;
