Definition s2p : poly A0 eqA ltM -> list (Term A n).

(* Specifications: *)
Theorem In_inp_inPolySet : forall (Q : list (poly A0 eqA ltM)) (p : poly A0 eqA ltM), In p Q -> ~ eqP A eqA n (s2p p) (pO A n) -> inPolySet (s2p p) Q.
Theorem in_inPolySet : forall (P : list (poly A0 eqA ltM)) (p : poly A0 eqA ltM), In p P -> ~ eqP A eqA n (s2p p) (pO A n) -> inPolySet (s2p p) P.
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).
Theorem inPolySet_inv1 : forall (P : list (poly A0 eqA ltM)) (p : list (Term A n)), inPolySet p P -> exists q : poly A0 eqA ltM, In q P /\ p = s2p q.
Theorem Incl_inp_inPolySet : forall P Q : list (poly A0 eqA ltM), incl P Q -> forall p : list (Term A n), inPolySet p P -> inPolySet p Q.