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Remark eqv_nimps_eq :
 forall ni1 ni2 : nested_imps,
 eqv_ni ni1 ni2 -> nested_imps2nimps ni1 = nested_imps2nimps ni2.

(* Specifications: *)
Lemma in_ngamma_eqv : forall (work : nf_list) (ds : disjs) (ni1 ni2 : nested_imps) (ai : atomic_imps) (a : atoms) (c : normal_form), eqv_ni ni1 ni2 -> in_ngamma work ds ni1 ai a c -> in_ngamma work ds ni2 ai a c.
Lemma in_ngamma_le : forall (work : nf_list) (ds : disjs) (ni1 ni2 : nested_imps) (ai : atomic_imps) (a : atoms) (c : normal_form), le_ni ni1 ni2 -> in_ngamma work ds ni1 ai a c -> in_ngamma work ds ni2 ai a c.
Lemma in_ngamma_ge : forall (work : nf_list) (ds : disjs) (ni1 ni2 : nested_imps) (ai : atomic_imps) (a : atoms) (c : normal_form), le_ni ni2 ni1 -> in_ngamma work ds ni1 ai a c -> in_ngamma work ds ni2 ai a c.