theorem Th40:
  for X be set, S be ZeroStr
    for p be Series of X,S, b be bag of X st b in Support p holds
       support b c= vars p
proof
  let X be set,S be ZeroStr;
  let p be Series of X,S, b be bag of X such that A1: b in Support p;
  set SS={support b where b is Element of Bags X:b in Support p};
  b in Bags X by PRE_POLY:def 12;
  then support b in SS by A1;
  then support b c= union SS by ZFMISC_1:74;
  hence thesis by Th39;
end;
