
theorem Th26:
  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) holds
  Support(Up(p,T,i)) c= Support(p) & Support(Low(p,T,i)) c= Support(p)
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);
  then Support(p|(Upper_Support(p,T,i))) = Upper_Support(p,T,i) & Support(p|(
  Lower_Support(p,T,i))) = Lower_Support(p,T,i) by Lm3;
  hence thesis by A1,Def2,Th24;
end;
