reserve i,j for Nat;
reserve A,B for Ring;
reserve K, L for Field;

theorem Th81:
  for f,g be Element of Polynom-Ring K holds
  f <> 0.Polynom-Ring K & {f}-Ideal is prime &
  not g in {f}-Ideal implies {f}-Ideal,{g}-Ideal are_co-prime
  proof
    let f,g be Element of Polynom-Ring K;
    {f,g}-Ideal = {f}-Ideal + {g}-Ideal by IDEAL_1:76;
    hence thesis by Th80;
  end;
