reserve i,j,k,n,m for Nat,
        b,b1,b2 for bag of n;

theorem Th7:
  for L being non empty ZeroStr, p being Series of n,L,
      b being bag of n+1 st b in Support (p extended_by_0)
  holds b.n = 0
proof
  let L be non empty ZeroStr,p be Series of n,L, b be bag of n+1;
  assume b in Support (p extended_by_0);
  then (p extended_by_0).b <>0.L by POLYNOM1:def 3;
  hence thesis by Def3;
end;
