unfold irreducible in |- *; auto.
intros Q q; red in |- *; intros H'; inversion H'.
Qed.
Hint Resolve pO_irreducible.

(* Specifications: *)
Theorem irreducible_eqp_com :
forall (Q : list (poly A0 eqA ltM)) (p q : list (Term A n)),
irreducible Q p ->
canonical A0 eqA ltM p -> eqP A eqA n p q -> irreducible Q q.