`{Funext} (O : Subuniverse) {T : Type} {U : Type} (f : T <~> U) : In O T <~> In O U := equiv_iff_hprop_uncurried (iff_inO_equiv _ f).
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.