intros Q a p H' H'0; elim H'0; auto.
intros a0 p0 q s H'1 H'2 H'3 H'4 H'5.
cut (canonical A0 eqA ltM q);
[ intros C0 | apply inPolySet_imp_canonical with (L := Q); auto ].
cut (canonical A0 eqA ltM p0);
[ intros Op1 | apply CombLinear_canonical with (Q := Q); auto ].
apply
CombLinear_1
with
(a := multTerm (A:=A) multA (n:=n) a a0)
(p := mults (A:=A) multA (n:=n) a p0)
(q := q); auto.
apply
(eqp_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := mults (A:=A) multA (n:=n) a
(pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM)
ltM_dec (mults (A:=A) multA (n:=n) a0 q) p0));
auto.
apply
(eqp_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec
(mults (A:=A) multA (n:=n) a (mults (A:=A) multA (n:=n) a0 q))
(mults (A:=A) multA (n:=n) a p0)); auto.
apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto.
Qed.
Hint Resolve CombLinear_mults1.

Theorem CombLinear_minuspf :
forall (Q : list (poly A0 eqA ltM)) (p : list (Term A n)),
CombLinear Q p ->
forall q : list (Term A n),
CombLinear Q q ->
CombLinear Q
(minuspf A A0 A1 eqA invA minusA multA eqA_dec n ltM ltM_dec p q).