intros i L L1 L2 H'; elim H'; simpl in |- *; auto with datatypes.
intros L0 L3 L4 L5 a i0 H'0 H'1 H'2.
unfold incl in |- *; simpl in |- *; auto.
Qed.

(* Specifications: *)
Lemma spolyp_cons_genPcP0 :
forall (aP R Q : list _) (i : poly A0 eqA ltM),
genPcP i aP R Q ->
~ BuchAux.zerop A A0 eqA n ltM i ->
forall b : poly A0 eqA ltM,
In b aP ->
~ BuchAux.zerop A A0 eqA n ltM b ->
exists c : poly A0 eqA ltM,
In c aP /\
(In
(spolyp A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM
ltM_dec os i c) Q \/ foreigner A A0 A1 eqA multA n ltM i c) /\
divp A A0 eqA multA divA n ltM
(ppcp A A0 A1 eqA plusA invA minusA multA divA cs n ltM i b) c.