`{Univalence} {F : Type} : BAut F <~> Type_ (subuniverse_merely_equiv F). Proof. srapply equiv_functor_sigma_id; intro X; cbn. rapply Trunc_functor_equiv. exact (equiv_path_universe _ _)^-1%equiv. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Constant. Require Import HoTT.Truncations. Require Import ObjectClassifier Homotopy.ExactSequence Pointed.