intros a b; (case a; case b).
intros x c0 x0 c1; generalize c0 c1; case x; case x0; simpl in |- *; auto.
intros a0 l a1 l0 H' H'0 H'1 H'2.
apply divP_ppcr with (1 := cs); auto.
apply canonical_nzeroP with (ltM := ltM) (p := l); auto.
apply canonical_nzeroP with (ltM := ltM) (p := l0); auto.
Qed.

Theorem divp_nzeropl : forall a b : poly A0 eqA ltM, divp a b -> ~ zerop a.
intros a b; (case a; case b).