
theorem Z2:
for R being non degenerated Ring
for n being Ordinal
for p being Polynomial of n,R
holds Support(LM p) = {} or Support(LM p) = {Lt p}
proof
let R be non degenerated Ring, n be Ordinal, p be Polynomial of n,R;
set m = LM p;
per cases by POLYNOM7:6;
suppose Support(LM p) = {};
  hence thesis;
  end;
suppose ex b being bag of n st Support(LM p) = {b};
  then consider b being bag of n such that H: Support(LM p) = {b};
  per cases;
  suppose Support p = {};
    then p = 0_(n,R) by YY;
    then Lt p = EmptyBag n & 0.R = p.b by defLT,POLYNOM1:22;
    then not b in Support p by POLYNOM1:def 4;
    then not b in Support(LM p) by YZ,TARSKI:def 3;
    hence thesis by H,TARSKI:def 1;
    end;
  suppose Support p <> {};
    then p <> 0_(n,R) by YY;
    then I: LC p is non zero by Y0;
    {b} = {term(m)} by H,POLYNOM7:7;
    then b in {term(m)} by TARSKI:def 1;
    then b = term(m) by TARSKI:def 1 .= Lt p by I,POLYNOM7:10;
    hence thesis by H;
    end;
  end;
end;
