
theorem Th24:
  for L being add-associative right_zeroed right_complementable
unital non empty doubleLoopStr for p being Polynomial of L st deg p = 0 holds
  not(p is with_roots)
proof
  let L be add-associative right_zeroed right_complementable unital non empty
  doubleLoopStr, p be Polynomial of L;
  assume
A1: deg p = 0;
  then
A2: p = <%p.0%> by ALGSEQ_1:def 5;
  now
    assume p is with_roots;
    then consider x be Element of L such that
A3: x is_a_root_of p by POLYNOM5:def 8;
    0.L = eval(p,x) by A3,POLYNOM5:def 7
      .= p.0 by A2,POLYNOM5:37;
    hence contradiction by A1,A2,ALGSEQ_1:14;
  end;
  hence thesis;
end;
