intros a; case a; simpl in |- *.
intros x; case x; auto.
intros c Q H'.
replace (nil (A:=Term A n)) with (pO A n); auto; apply CombLinear_0; auto.
intros a0 l c Q H'.
apply CombLinear_id with (1 := cs); auto.
change
(inPolySet A A0 eqA n ltM
(s2p A A0 eqA n ltM (mks A A0 eqA n ltM (pX a0 l) c)) Q)
in |- *; apply in_inPolySet; auto.
red in |- *; intros H'4; inversion H'4.
Qed.

Theorem inPolySet_addEnd :
forall (a : list (Term A n)) (p : poly A0 eqA ltM)
(l : list (poly A0 eqA ltM)),
inPolySet A A0 eqA n ltM a (addEnd p l) ->
a = s2p A A0 eqA n ltM p \/ inPolySet A A0 eqA n ltM a l.