intros a b c H' H'0; inversion H'0; inversion H'.
intros H'1 H'2; apply divTerm_def with (nZb := nZb0); auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := plusTerm (A:=A) plusA (n:=n)
(multTerm (A:=A) multA (n:=n) (divTerm a nZb0) c)
(multTerm (A:=A) multA (n:=n) (divTerm b nZb0) c));
auto.
apply eqTerm_plusTerm_comp with (1 := cs); auto.
apply multTerm_eqT; auto.
apply eqT_divTerm; auto.
apply (eqT_refl A n).
apply (eqT_refl A n).
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := multTerm (A:=A) multA (n:=n)
(plusTerm (A:=A) plusA (n:=n) (divTerm a nZb0) (divTerm b nZb0))
c); auto.
apply multTerm_plusTerm_dist_l with (1 := cs); auto.
apply eqTerm_multTerm_comp with (1 := cs); auto.
apply (eqTerm_sym _ _ _ _ _ _ _ _ _ cs n); auto.
apply eqT_divTerm_plusTerm; auto.
Qed.
Hint Resolve divP_plusTerm.

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