intros x; case x.
intros c; left; simpl in |- *; auto.
intros a l c; right; red in |- *; intros H'0; inversion H'0.
Qed.
Definition divp : poly A0 eqA ltM -> poly A0 eqA ltM -> Prop.
intros H'; case H'.
intros x; case x.
intros H'0 H'1; exact False.
intros a l H'0 H'1; case H'1.
intros x0; case x0.
intros H'2; exact False.
intros a0 l0 H'2.
exact (divP A A0 eqA multA divA n a a0).
Defined.

Theorem divp_trans : transitive (poly A0 eqA ltM) divp.
red in |- *.