
theorem
  for n being set, a, b being bag of n
  st b divides a holds support b c= support a
proof
  let n be set, a, b be bag of n such that
A1: b divides a;
  let x be object;
  assume x in support b;
  then b.x <> 0 by PRE_POLY:def 7;
  then a.x <> 0 by A1,PRE_POLY:def 11;
  hence thesis by PRE_POLY:def 7;
end;
