intros a b Q H'; elim H'; auto.
intros x y H'0 H'1 x0 H'2.
apply CombLinear_comp with (p := y); auto.
rewrite <- H'2; case x0; simpl in |- *; auto.
intros x1; case x1; simpl in |- *; auto.
intros t l c; apply CombLinear_id; auto.
change
(inPolySet A A0 eqA n ltM (pX t l)
(exist (fun l0 => canonical A0 eqA ltM l0) (pX t l) c :: Q))
in |- *; apply incons; auto.
apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto.
intros x y z H'0 H'1 H'2 H'3 x0 H'4.
lapply H'2;
[ intros H'5; lapply (H'5 x0); [ intros H'7; clear H'2 | clear H'2 ]
| clear H'2 ]; auto.
cut (canonical A0 eqA ltM y).
intros H'2.
lapply (reduce_cb2 (mks A A0 eqA n ltM x H'3) (mks A A0 eqA n ltM y H'2) Q);
simpl in |- *; [ intros H'9 | idtac ]; auto.
apply
CombLinear_trans_cons_lem
with
(R := mks A A0 eqA n ltM y H'2 :: x0 :: Q)
(b := mks A A0 eqA n ltM y H'2); auto.
apply CombLinear_incl with (P := mks A A0 eqA n ltM y H'2 :: Q); auto.
intros a0 H'6.
apply Incl_inp_inPolySet with (P := mks A A0 eqA n ltM y H'2 :: Q); auto.
red in |- *; simpl in |- *; auto with datatypes.
intros a1 H'8; elim H'8; auto.
apply canonical_reduce with (1 := cs) (3 := H'0); auto.
apply canonical_reduce with (1 := cs) (3 := H'0); auto.
Qed.

Theorem reduceplus_cb2 :
forall (a b : poly A0 eqA ltM) (Q : list (poly A0 eqA ltM)),
reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
(s2p A A0 eqA n ltM a) (s2p A A0 eqA n ltM b) ->
CombLinear (b :: Q) (s2p A A0 eqA n ltM a).