
theorem Th29:
  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 iff not q < p,
  T
proof
  let n be Ordinal, T be connected TermOrder of n, L be non empty addLoopStr,
  p,q being Polynomial of n,L;
A1: not q < p,T implies p <= q,T
  proof
    assume
A2: not q < p,T;
    now
      per cases by A2;
      case
        not Support q <> Support p;
        hence thesis by Th26;
      end;
      case
        not q <= p,T;
        hence thesis by Th28;
      end;
    end;
    hence thesis;
  end;
  p <= q,T implies not q < p,T
  by Th26;
  hence thesis by A1;
end;
