intros a b H' nZb H'1; apply divTerm_def with (nZb := nZb); auto.
apply divTerm_on_eqT; auto.
Qed.

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).