intros a b H' nZa; red in |- *; intros H'1; auto.
case H';
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (y := multA (divA b a nZa) a);
auto.
apply divA_is_multA with (1 := cs); auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (y := multA A0 a); auto.
apply multA_eqA_comp with (1 := cs); auto.
apply (eqA_ref _ _ _ _ _ _ _ _ _ cs); auto.
apply multA_A0_l with (1 := cs); auto.
Qed.
Hint Resolve divA_nZ.

Theorem unit_nZ :
forall p : poly A0 eqA ltM, ~ zeroP (A:=A) A0 eqA (n:=n) (unit p).