intros x y z; case x; case y; case z.
intros x0 c x1 c0 x2 c1; generalize c c0 c1; case x0; case x1; case x2;
simpl in |- *; auto.
intros a l a0 l0 H' H'0 H'1 H'2; elim H'2.
intros a l a0 l0 a1 l1 H' H'0 H'1 H'2 H'3.
apply (divP_trans _ _ _ _ _ _ _ _ _ cs n) with (y := a0); auto.
Qed.

Theorem divp_dec : forall a b : poly A0 eqA ltM, {divp a b} + {~ divp a b}.
intros a b; case a; case b.