intros P; elim P; auto.
intros p H'; inversion H'.
simpl in |- *.
intros a l H' p H'0; elim H'0;
[ intros H'1; rewrite <- H'1; clear H'0 | intros H'1; clear H'0 ];
auto.
case a; simpl in |- *.
intros x; case x; auto.
intros c H'0; elim H'0; auto.
intros t l0 c H;
change (inPolySet (pX t l0) (exist (canonical A0 eqA ltM) (pX t l0) c :: l))
in |- *; apply incons.
Qed.

(* Specifications: *)
Theorem inPolySet_inv0 :
forall (P : list (poly A0 eqA ltM)) (p : list (Term A n)),
inPolySet p P -> ~ eqP A eqA n p (pO A n).