
theorem Th7:
  for n being Ordinal, T being admissible connected TermOrder of n,
  L being right_zeroed add-associative right_complementable well-unital
distributive non trivial doubleLoopStr, p,q being Polynomial of n,L
  holds HT(p-q,T) <= max(HT(p,T),HT(q,T),T), T
proof
  let n be Ordinal, T be admissible connected TermOrder of n, L be
right_zeroed add-associative right_complementable well-unital distributive non
  trivial non empty doubleLoopStr, p,q being Polynomial of n,L;
  HT(p+(-q),T) <= max(HT(p,T),HT(-q,T),T),T by TERMORD:34;
  then HT(p-q,T) <= max(HT(p,T),HT(-q,T),T),T by POLYNOM1:def 7;
  hence thesis by Th6;
end;
