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_plusTerm_z : forall (a b c : Term A n) (nZc : ~ zeroP (A:=A) A0 eqA (n:=n) c) (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 c -> divP A A0 eqA multA divA n b c -> eqT a b -> zeroP (A:=A) A0 eqA (n:=n) (plusTerm (A:=A) plusA (n:=n) a b) -> eqP A eqA n (pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec p q) (pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec (spminusf a c nZc p r) (spminusf b c nZc q r)).