
theorem
for L be Abelian add-associative right_zeroed right_complementable
         well-unital associative distributive commutative
         almost_left_invertible domRing-like non trivial doubleLoopStr
for z be non zero rational_function of L
for z1 being rational_function of L,
    z2 being non zero Polynomial of L
st z = [z2 *' z1`1, z2 *' z1`2] & z1 is irreducible &
   ex f being FinSequence of Polynom-Ring(L)
   st z2 = Product f &
      for i being Element of NAT st i in dom f
      ex x being Element of L st x is_a_common_root_of z`1,z`2 &
                                 f.i = rpoly(1,x)
holds NF z = NormRationalFunction z1 by Def17;
