intros a b p; case p; auto.
intros H' H'0.
change (canonical A0 eqA ltM (pX a (pO A n))) in |- *; apply canonicalp1;
auto.
apply divP_inv1 with (1 := H'0); auto.
intros a0 l H' H'0; change (canonical A0 eqA ltM (pX a (pX a0 l))) in |- *;
apply canonical_cons; auto.
case (ltT_dec A n ltM ltM_dec a b);
[ intros tmp; case tmp; clear tmp | idtac ]; intros H'2;
auto.
elim (divP_is_not_order a b); auto.
apply (ltT_trans A _ _ os) with (y := b); auto.
apply (canonical_pX_order _ A0 eqA) with (l := l); auto.
apply eqT_compat_ltTr with (b := b); auto.
apply (eqT_sym A n); auto.
apply (canonical_pX_order _ A0 eqA) with (l := l); auto.
apply divP_inv1 with (1 := H'0); auto.
apply canonical_imp_canonical with (a := b); auto.
Qed.
Definition spminusf (a b : Term A n) (nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b)
(p q : list (Term A n)) :=
minuspf A A0 A1 eqA invA minusA multA eqA_dec n ltM ltM_dec p
(mults (A:=A) multA (n:=n)
(divTerm (A:=A) (A0:=A0) (eqA:=eqA) divA (n:=n) a (b:=b) nZb) q).

(* Specifications: *)
Theorem sp_rew :
forall (a b : Term A n) (nZ1 nZ2 : ~ zeroP (A:=A) A0 eqA (n:=n) b)
(p q : list (Term A n)), spminusf a b nZ1 p q = spminusf a b nZ2 p q.