reserve n for Nat;

theorem
for F being domRing,
    p,q being Polynomial of F
for a being Element of F
st rpoly(1,a) divides (p*'q) holds rpoly(1,a) divides p or rpoly(1,a) divides q
proof
let L be domRing, p,q be Polynomial of L; let x be Element of L;
assume rpoly(1,x) divides (p*'q);
then eval(p*'q,x) = 0.L by Th9;
then A1: eval(p,x) * eval(q,x) = 0.L by POLYNOM4:24;
per cases by A1,VECTSP_2:def 1;
suppose eval(p,x) = 0.L;
  hence thesis by Th9;
  end;
suppose eval(q,x) = 0.L;
  hence thesis by Th9;
  end;
end;
