Inductive divP : Term A n -> Term A n -> Prop :=
    divTerm_def :
      forall a b : Term A n,
      ~ zeroP (A:=A) A0 eqA (n:=n) a ->
      forall nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b,
      eqTerm (A:=A) eqA (n:=n) a
        (multTerm (A:=A) multA (n:=n) (divTerm a nZb) b) -> 
      divP a b.Inductive divP : Term A n -> Term A n -> Prop :=
    divTerm_def :
      forall a b : Term A n,
      ~ zeroP (A:=A) A0 eqA (n:=n) a ->
      forall nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b,
      eqTerm (A:=A) eqA (n:=n) a
        (multTerm (A:=A) multA (n:=n) (divTerm a nZb) b) -> 
      divP a b.

Theorem divP_invTerm_r : forall a b : Term A n, divP a b -> divP a (invTerm (A:=A) invA (n:=n) b).