intros a b; case a; case b; simpl in |- *; auto.
intros b2 c2 b3 c3.
intros Zp1 Zp2.
case (mk_clean c3 c2).
intros x; case x.
intros c b4; case b4.
intros H0; left; simpl in |- *; auto.
generalize (div_clean_dec1 n c3 c2); rewrite <- H0; simpl in |- *; auto.
intros H1; case H1; auto; intros H2 H3; split; auto.
apply divA_is_multA with (1 := cs); auto.
intros H0; right; red in |- *; intros dviP_H; inversion dviP_H.
generalize (div_clean_dec2 n c3 c2); simpl in |- *; auto.
intros H'; lapply H'; [ intros H'0; apply H'0; clear H' | clear H' ].
rewrite <- H1; auto.
rewrite <- H0; simpl in |- *; auto.
Qed.

Theorem zeroP_divTerm :
forall a b : Term A n,
zeroP (A:=A) A0 eqA (n:=n) a ->
forall nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b,
zeroP (A:=A) A0 eqA (n:=n) (divTerm a nZb).