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

theorem
  for b be bag of X st n <> 0 holds support (n(#)b) = support b
proof
  let b be bag of X such that
A1: n<>0;
  thus support (n(#)b) c= support b by Th7;
  let x be object;
  assume x in  support b;
  then
A2: b.x<>0 by PRE_POLY:def 7;
  (n(#)b).x = n * (b.x) by VALUED_1:6;
  hence thesis by A1,A2,PRE_POLY:def 7;
end;
