
theorem Th24:
  for L being add-associative right_zeroed right_complementable
  distributive non empty doubleLoopStr, p, q being (Polynomial of L) st p-q =
  0_. L holds p = q
proof
  let L be add-associative right_zeroed right_complementable distributive non
  empty doubleLoopStr, q, r be (Polynomial of L);
  set PRL = Polynom-Ring L;
  reconsider qc = q, rc = r as Element of PRL by POLYNOM3:def 10;
  assume
A1: q-r = 0_. L;
  0_. L = 0.PRL by POLYNOM3:def 10;
  then qc-rc = 0.PRL by A1,Th22;
  hence thesis by VECTSP_1:27;
end;
