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).

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).