
theorem Th21:
  for L being add-associative right_zeroed right_complementable
  distributive non empty doubleLoopStr, p being (Polynomial of L), pc being (
  Element of Polynom-Ring L) st p = pc holds -p = -pc
proof
  let L be add-associative right_zeroed right_complementable distributive non
empty doubleLoopStr, p be (Polynomial of L), pc be (Element of Polynom-Ring L)
  such that
A1: p = pc;
  set PRL = Polynom-Ring L;
  reconsider mpc = -p as Element of PRL by POLYNOM3:def 10;
  p+-p = p-p .= 0_. L by POLYNOM3:29;
  then pc + mpc = 0_. L by A1,POLYNOM3:def 10
    .= 0.PRL by POLYNOM3:def 10;
  hence thesis by RLVECT_1:def 10;
end;
