intros a b c nZc p q r H' H'0 H'1 H'2 H'3 H'4.
apply (eqp_trans _ _ _ _ _ _ _ _ _ cs n) with (y := spminusf b c nZc p r);
auto.
apply eqTerm_spminusf_com; auto.
apply eqptail_spminusf_com; auto.
apply divP_eqTerm_comp with (1 := cs) (a := a); auto.
Qed.
Hint Resolve eqTerm_spminusf_com eqp_spminusf_com eqp_spminusf_com.

Theorem spminusf_minuspf :
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
(spminusf a b nZb p r) q).