intros a b nZb p q r H' H'0 H'1 H'2.
apply
(eqp_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec
(spminusf a b nZb p r) q); [ auto | idtac ].
apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto.
Qed.

(* Specifications: *)
Theorem spminusf_minusTerm_r :
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
(minuspf A A0 A1 eqA invA minusA multA eqA_dec n ltM ltM_dec p q) r)
(minuspf A A0 A1 eqA invA minusA multA eqA_dec n ltM ltM_dec p
(spminusf (invTerm (A:=A) invA (n:=n) a) b nZb q r)).