(** The other components of ggcd are indeed the correct factors. *)

Ltac destr_pggcdn IHn :=
 match goal with |- context [ ggcdn _ ?x ?y ] =>
  generalize (IHn x y); destruct ggcdn as (?g,(?u,?v)); simpl
 end.

Lemma gcd_divide_r : forall a b, (gcd a b | b).