
theorem Th30:
  for L being add-associative right_zeroed right_complementable
  well-unital Abelian non degenerated non empty doubleLoopStr for z being
  Element of L holds z is_a_root_of rpoly(1,z)
proof
  let L be Abelian well-unital add-associative right_zeroed non degenerated
  right_complementable non empty doubleLoopStr, z be Element of L;
  eval(rpoly(1,z),z) = z - z by Th29
    .= 0.L by RLVECT_1:15;
  hence thesis by POLYNOM5:def 7;
end;
