(X A : Type) : BAut X -> BAut (X * A) := fun Z:BAut X => (Z * A ; Trunc_functor (-1) (ap (fun W => W * A)) (pr2 Z)) : BAut (X * A).
Require Import HoTT.Basics HoTT.Types. Require Import Constant. Require Import HoTT.Truncations. Require Import ObjectClassifier Homotopy.ExactSequence Pointed.