`{Univalence} X `{IsTrunc 1 X} : center2_baut X (exist (fun (f:forall x:X, x=x) => forall (g:X<~>X) (x:X), ap g (f x) = f (g x)) (fun x => idpath x) (fun (g:X<~>X) (x:X) => idpath (idpath (g x)))) = fun Z => idpath (idpath Z). Proof. apply path_forall; intros Z. assert (IsHSet (idpath Z.1 = idpath Z.1)) by exact _. baut_reduce. cbn. unfold functor_forall, sig_rect, merely_rec_hset. cbn. rewrite equiv_path2_universe_1. rewrite !concat_p1, !concat_Vp. simpl. rewrite !concat_p1, !concat_Vp. reflexivity. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Constant. Require Import HoTT.Truncations. Require Import ObjectClassifier Homotopy.ExactSequence Pointed.