apply divA_eqA_comp with (1 := cs); auto.
apply eqA_trans with (y := multA A0 (divA a a nZa)); auto.
Qed.
Hint Resolve divA_A0_l.

Theorem A_sep : forall a b : A, eqA (multA a b) A0 -> eqA a A0 \/ eqA b A0.
intros a b H'; case (eqA_dec a A0); auto; case (eqA_dec b A0); auto.