reserve i,j,k,n,m for Nat,
        X for set,
        b,s for bag of X,
        x for object;

theorem Th13:
  for X be set,x,i st x in X & i <>0 holds
    support((EmptyBag X) +*(x,i))={x}
proof
  let X be set,x,i  such that
A1: x in X & i <> 0;
  reconsider i as Element of NAT by ORDINAL1:def 12;
  reconsider D=X as non empty set by A1;
  reconsider d=x as Element of D by A1;
  (EmptyBag X) +*(x,i) = ({d},i)-bag by Th12;
  hence thesis by A1,UPROOTS:8;
end;
