(T:Type) : IsEquiv (to O T) -> In O T := fun _ => inO_equiv_inO (O T) (to O T)^-1.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.