
theorem Th32: :: lemma 5.17 (iii), 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 HC(p*'q,T) = HC(p,T) * HC(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 HC(p*'q,O) = (p*'q).(HT(p,O) + HT(q,O)) by Th31
    .= HC(p,O) * HC(q,O) by Lm14;
end;
