
theorem :: lemma 5.17 (ii), p. 195
  for n being Ordinal, T being admissible connected TermOrder of n, L
  being add-associative right_complementable right_zeroed well-unital
  distributive domRing-like non trivial doubleLoopStr, p,q being non-zero
  Polynomial of n,L holds HM(p*'q,T) = HM(p,T) *' HM(q,T)
proof
  let n be Ordinal, O being admissible connected TermOrder of n, L be
  add-associative right_complementable right_zeroed well-unital distributive
  domRing-like non trivial doubleLoopStr, p,q be non-zero Polynomial of n,L;
  thus HM(p*'q,O) = Monom(HC(p,O) * HC(q,O),HT(p*'q,O)) by Th32
    .= Monom(HC(p,O) * HC(q,O),HT(p,O) + HT(q,O)) by Th31
    .= HM(p,O) *' HM(q,O) by Th3;
end;
