
theorem Th29:
  for n being Ordinal, T being connected TermOrder of n, L being
  add-associative right_zeroed right_complementable non empty addLoopStr, p
being Polynomial of n,L, i being Element of NAT st i <= card(Support p) for b,
b9 being bag of n st b in Support Low(p,T,i) & b9 in Support Up(p,T,i) holds b
  < b9,T
proof
  let n be Ordinal, T be connected TermOrder of n, L be add-associative
right_zeroed right_complementable non empty addLoopStr, p be Polynomial of n,
  L, i be Element of NAT;
  assume
A1: i <= card(Support p);
  let b,b9 be bag of n;
  assume
A2: b in Support Low(p,T,i) & b9 in Support Up(p,T,i);
  Support Up(p,T,i) = Upper_Support(p,T,i) & Support Low(p,T,i) =
  Lower_Support(p,T,i) by A1,Lm3;
  hence thesis by A1,A2,Th20;
end;
