unfold red in |- *.
intros a p q H' H'0.
inversion H'0.
apply rstar_rtopO; auto.
case a; auto.
apply inP_reducestar with (Q := p); auto.
intros a0 H'1.
apply Incl_inp_inPolySet with (P := p); auto.
Qed.
Definition zerop : poly A0 eqA ltM -> Prop.
intros H'; case H'.
intros x; case x.
intros H'0; exact True.
intros a l H'0; exact False.
Defined.

(* Specifications: *)
Theorem zerop_dec : forall a : poly A0 eqA ltM, {zerop a} + {~ zerop a}.
intros H'; case H'.