
theorem Th16:
  for n being Ordinal, T being connected admissible TermOrder of n
  , L being non empty ZeroStr, p being Polynomial of n,L, b,b9 being bag of n
  holds b9 in Support(b*'p) implies b9 <= b+HT(p,T),T
proof
  let n be Ordinal, T be connected admissible TermOrder of n, L be non empty
  ZeroStr, p be Polynomial of n,L, b,b9 be bag of n;
  assume
A1: b9 in Support(b*'p);
  Support(b*'p) c= {b + b2 where b2 is Element of Bags n : b2 in Support p
  } by Lm10;
  then b9 in {b + b2 where b2 is Element of Bags n : b2 in Support p} by A1;
  then consider s being Element of Bags n such that
A2: b9 = b + s and
A3: s in Support p;
  s <= HT(p,T),T by A3,TERMORD:def 6;
  then [s,HT(p,T)] in T by TERMORD:def 2;
  then [b+s,b+HT(p,T)] in T by BAGORDER:def 5;
  hence thesis by A2,TERMORD:def 2;
end;
