unfold spminusf in |- *.
intros a b nZb p q H' H'0 H'1; try assumption.
inversion H'1.
apply order_minuspf with (1 := cs); auto.
apply
canonical_pX_eqT
with
(a := multTerm (A:=A) multA (n:=n)
(divTerm (A:=A) (A0:=A0) (eqA:=eqA) divA (n:=n) a (b:=b) nZb) b);
auto.
change
(canonical A0 eqA ltM
(mults (A:=A) multA (n:=n) (divTerm divA a nZb) (pX b q)))
in |- *; auto.
apply (eqT_sym A n); apply (eqTerm_imp_eqT A eqA n); auto.
Qed.
Hint Resolve canonical_spminusf_full_t.

(* Specifications: *)
Theorem spminusf_pluspf :
forall (a b : Term A n) (nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b)
(p q r : list (Term A n)),
canonical A0 eqA ltM p ->
canonical A0 eqA ltM q ->
canonical A0 eqA ltM r ->
divP A A0 eqA multA divA n a b ->
eqP A eqA n
(spminusf a b nZb
(pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec p
q) r)
(pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec
(spminusf a b nZb p r) q).