intros a b H'; inversion H'; auto.
apply divTerm_def with (nZb := nZb); auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := multTerm (A:=A) multA (n:=n)
(invTerm (A:=A) invA (n:=n) (divTerm a nZb)) b);
auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := invTerm (A:=A) invA (n:=n)
(multTerm (A:=A) multA (n:=n) (divTerm a nZb) b));
auto.
apply (eqTerm_sym _ _ _ _ _ _ _ _ _ cs n);
apply mult_invTerm_com with (1 := cs); auto.
apply eqTerm_multTerm_comp with (1 := cs); auto.
apply (eqTerm_sym _ _ _ _ _ _ _ _ _ cs n); apply divTerm_invTerm_l; auto.
Qed.
Hint Resolve divP_invTerm_l.

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