intros p L1 H'; elim H'; auto.
intros a p0 q s H'0 H'1 H'2 H'3 H'4 L2 H'5.
apply
CombLinear_comp
with
(p := pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec
(mults (A:=A) multA (n:=n) a q) p0); auto.
apply
eqp_imp_canonical
with
(1 := cs)
(p := pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec
(mults (A:=A) multA (n:=n) a q) p0); auto.
apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto.
apply canonical_pluspf; auto.
apply canonical_mults with (1 := cs); auto.
apply inPolySet_imp_canonical with (L := L1); auto.
apply CombLinear_canonical with (1 := H'2); auto.
apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto.
Qed.

Theorem reduceplus_cb1_lem :
forall (a b : list (Term A n)) (Q : list (poly A0 eqA ltM)),
reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q a b ->
forall x : poly A0 eqA ltM,
s2p A A0 eqA n ltM x = a -> CombLinear (x :: Q) b.