Lemma first_iso_nat_in_F: is_nat_trans Fun1 (exp (Yon c)) (λ F, make_nat_trans (pr1 (Fun1 F)) _ (first_iso_on_sets F) (first_iso_nat_in_x F)). Proof. intros X Y f. apply (nat_trans_eq has_homsets_HSET); intros x. apply funextsec; intros g. apply (nat_trans_eq has_homsets_HSET); intros y. now apply funextsec. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.RightKanExtension. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.YonedaBinproducts. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Presheaf.