
theorem Th28:
  for n being Ordinal, T being connected TermOrder of n, L being
  non empty addLoopStr, p,q being Polynomial of n,L holds p <= q,T or q <= p,T
proof
  let n be Ordinal, T be connected TermOrder of n, L be non empty addLoopStr,
  p,q be Polynomial of n,L;
  set R = RelStr(# Bags n, T#), O = RelStr (# Fin the carrier of R, FinOrd R
  #);
  reconsider sp = Support p, sq = Support q as Element of O by Lm11;
  FinPoset R is connected;
  then O is connected by BAGORDER:def 16;
  then sp <= sq or sq <= sp by WAYBEL_0:def 29;
  then
  [Support p, Support q] in FinOrd R or [Support q, Support p] in FinOrd R
  by ORDERS_2:def 5;
  hence thesis;
end;
