unfold irreducible in |- *.
intros Q a p H' H'0 q; red in |- *; intros H'1.
inversion_clear H'1.
apply
H'0
with
(q := spminusf A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec
a b nZb p q0); auto.
inversion_clear H; auto.
Qed.

(* Specifications: *)
Lemma pO_irreducible :
forall Q : list (poly A0 eqA ltM), irreducible Q (pO A n).