
theorem Th10:
  for X being set, L being non trivial ZeroStr, a being non zero
  Element of L, b being bag of X holds term(Monom(a,b)) = b
proof
  let n be set, L be non trivial ZeroStr, a be non zero Element of L, b be
  bag of n;
  set m = 0_(n,L)+*(b,a);
  reconsider m as Function of Bags n, the carrier of L;
  reconsider m as Function of Bags n, L;
  reconsider m as Series of n, L;
A1: b in Bags n by PRE_POLY:def 12;
A2: b in dom(b .--> a) by TARSKI:def 1;
  dom(0_(n,L)) = dom((Bags n) --> 0.L) by POLYNOM1:def 8
    .= Bags n;
  then m.b = (0_(n,L)+*(b .--> a)).b by A1,FUNCT_7:def 3
    .= (b .--> a).b by A2,FUNCT_4:13
    .= a by FUNCOP_1:72;
  then m.b <> 0.L;
  hence thesis by Def5;
end;
