intros a b; case a; case b; unfold eqT in |- *; simpl in |- *; auto.
intros d c A0' c0 H' H'0 H'1; rewrite <- H'1.
split; auto.
apply divA_is_multA with (1 := cs); auto.
rewrite mult_div_id; auto.
rewrite mult_mon_zero_l; auto.
Qed.

Theorem divTerm_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).