intros a b c H' H'0.
cut (~ zeroP (A:=A) A0 eqA (n:=n) c); [ intros nZc | auto ].
apply divTerm_def with (nZb := nZc); auto.
apply nzeroP_comp_eqTerm with (1 := cs) (a := a); auto.
apply divP_inv1 with (b := c); auto.
2: apply divP_inv2 with (a := a); auto.
apply
(eqTerm_trans _ _ _ _ _ _ _ _ _ cs n)
with (y := multTerm (A:=A) multA (n:=n) (divTerm a nZc) c);
auto.
apply (eqTerm_trans _ _ _ _ _ _ _ _ _ cs n) with (y := a); auto.
apply (eqTerm_sym _ _ _ _ _ _ _ _ _ cs n); auto.
Qed.

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