Lemma homset_conj_inv_after_conj {c : C} {c' : C'} {g : C⟦c, G c'⟧} (d : D c) {d' : D' c'} (beta : FF _ d -->[#F g · ε _] d') : homset_conj_inv _ _ _ (homset_conj _ _ _ beta) = beta. Proof. unfold homset_conj. rewrite <- homset_conj_inv_after_conj'. unfold homset_conj_inv. rewrite disp_functor_transportf. rewrite mor_disp_transportf_postwhisker. apply maponpaths_2, homset_property. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences.