intros a b nZa nZb.
apply divTerm_def with (nZb := nZa); auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := multTerm (A:=A) multA (n:=n)
(multTerm (A:=A) multA (n:=n) (divTerm a nZa) b) a);
auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with
(y := multTerm (A:=A) multA (n:=n)
(multTerm (A:=A) multA (n:=n) (T1 A1 n) b) a);
auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with (y := multTerm (A:=A) multA (n:=n) b a); auto.
apply eqTerm_multTerm_comp with (1 := cs); auto.
apply eqTerm_multTerm_comp with (1 := cs); auto.
apply (eqTerm_sym _ _ _ _ _ _ _ _ _ cs n); apply div_is_T1; auto.
apply eqTerm_multTerm_comp with (1 := cs); auto.
apply (eqTerm_sym _ _ _ _ _ _ _ _ _ cs n); apply divTerm_multTerm_r; auto.
Qed.

Theorem divTerm_multTermr :
forall a b : Term A n,
~ zeroP (A:=A) A0 eqA (n:=n) a ->
~ zeroP (A:=A) A0 eqA (n:=n) b -> divP (multTerm (A:=A) multA (n:=n) a b) b.