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_extend : forall (a b : Term A n) (nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b) (p q : list (Term A n)), divP A A0 eqA multA divA n a b -> canonical A0 eqA ltM (pX a p) -> canonical A0 eqA ltM (pX b q) -> eqP A eqA n (spminusf a b nZb p q) (spminusf a b nZb (pX a p) (pX b q)).