
:: theorem 5.12, p. 193
  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 & q <= p,T iff
  Support p = Support q
proof
  let n be Ordinal, T be connected TermOrder of n, L be non empty addLoopStr,
  p,q being Polynomial of n,L;
  set O = FinOrd RelStr(# Bags n, T#);
A1: now
    assume p <= q,T & q <= p,T;
    then
A2: [Support p, Support q] in O & [Support q, Support p] in O;
    Support p in Fin the carrier of RelStr(# Bags n, T#) & Support q in
    Fin the carrier of RelStr(# Bags n, T#) by Lm11;
    hence Support p = Support q by A2,ORDERS_1:4;
  end;
  Support p = Support q implies p <= q,T & q <= p,T by Lm11,ORDERS_1:3;
  hence thesis by A1;
end;
