intros ni1 ni2 eqv12; elim eqv12; clear eqv12 ni1 ni2.
apply Eqv_NI_Nil.
intros x ni1 ni2 eqv12 ih; apply Eqv_NI_Cons_NN; assumption.
intros x k ni1 ni2 eqv12 ih; apply Eqv_NI_Cons_ND; assumption.
intros x k k' ni1 ni2 eqv12 ih; apply Eqv_NI_Cons_DD; assumption.
intros x k ni1 ni2 eqv12 ih; apply Eqv_NI_Cons_DN; assumption.
Qed.

Lemma ge_eqv : forall ni1 ni2 : nested_imps, le_ni ni2 ni1 -> eqv_ni ni1 ni2.
intros ni1 ni2 le21.