`{Funext} A (c : forall i (f : acc_ngen O i -> A), NullHomotopy f) : In O A. Proof. apply (snd (inO_iff_isnull O A)); intros i. apply ((equiv_ooextendable_isequiv _ _)^-1%equiv). snrapply isequiv_adjointify. - intros f []; exact (c i f).1. - intros f; apply path_arrow; intros x. simpl; unfold composeD. symmetry; exact ((c i f).2 x). - intros g; apply path_arrow; intros []. pose ((c i (g oD (null_to_local_generators (acc_ngen O)) i)).2). simpl in p; unfold composeD in p. symmetry; apply p, inhab. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Extensions NullHomotopy. Require Import Modality. Module Import IsLocal_Internal. Module Import IsNull_Internal.