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_on_eqT_eqT : forall a b : Term A n, ~ zeroP (A:=A) A0 eqA (n:=n) a -> forall nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b, eqT a b -> eqT (divTerm a nZb) (T1 A1 n).