Lemma homset_conj'_after_conj'_inv {c : C} {c' : C'} (f : C'⟦F c, c'⟧) (d : D c) (d' : D' c') (alpha : d -->[η _ · #G f] GG _ d') : homset_conj' _ _ _ (homset_conj'_inv _ _ _ alpha) = alpha. Proof. unfold homset_conj', homset_conj'_inv. rewrite disp_functor_transportf. rewrite mor_disp_transportf_prewhisker. rewrite <- homset_conj'_after_conj_inv. 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.