
theorem
  for n being Ordinal, L being domRing-like non trivial doubleLoopStr,
  p being Polynomial of n,L, a being non zero Element of L holds Support(p) c=
  Support(a*p)
proof
  let n be Ordinal, L be domRing-like non trivial doubleLoopStr, p be
  Polynomial of n,L, a be non zero Element of L;
  now
    let u be object;
    assume
A1: u in Support p;
    then reconsider u9 = u as Element of Bags n;
A2: (a*p).u9 = a * p.u9 & a <> 0.L by POLYNOM7:def 9;
    p.u9 <> 0.L by A1,POLYNOM1:def 4;
    then (a*p).u9 <> 0.L by A2,VECTSP_2:def 1;
    hence u in Support(a*p) by POLYNOM1:def 4;
  end;
  hence thesis by TARSKI:def 3;
end;
