
theorem Th7:
  for X being set, L being non empty ZeroStr, m being Monomial of X
  ,L holds Support(m) = {} or Support(m) = {term(m)}
proof
  let X be set, L be non empty ZeroStr, m be Monomial of X,L;
A1: term(m) is Element of Bags X by PRE_POLY:def 12;
  assume
A2: Support(m) <> {};
  then m.term(m) <> 0.L by Def5;
  then
A3: term(m) in Support(m) by A1,POLYNOM1:def 4;
  ex b being bag of X st Support(m) = {b} by A2,Th6;
  hence thesis by A3,TARSKI:def 1;
end;
