
theorem lemma2y:
for F being Field
for G being non empty FinSequence of the carrier of Polynom-Ring F
st for i being Nat st i in dom G
   ex a being Element of F st G.i = rpoly(1,a)
holds G is Factorization of (Product G)
proof
let F be Field;
let G be non empty FinSequence of the carrier of Polynom-Ring F;
assume A: for i being Nat st i in dom G
          ex a being Element of F st G.i = rpoly(1,a);
C:now let i be Element of dom G;
  consider a being Element of F such that B: G.i = rpoly(1,a) by A;
  deg rpoly(1,a) = 1 by HURWITZ:27;
  hence G.i is irreducible by B,RING_4:42;
  end;
then B: G is_a_factorization_of (Product G) by RING_2:def 11;
(Product G) is factorizable by C,RING_2:def 11,RING_2:def 12;
hence thesis by B,RING_2:def 13;
end;
