Definition disp_cat_eq_step_6_left : disp_cat_eq_functor → ∑ (F : disp_functor (functor_identity C) D₁ D₂), (∏ (x : C), isweq (F x)) × disp_functor_ff F. Proof. intro FF. simple refine (_ ,, _ ,, _). - simple refine ((_ ,, _) ,, (_ ,, _)). + exact (λ x, pr1 FF x). + exact (λ x y xx yy f ff, pr12 FF x y xx yy f ff). + exact (λ x xx, pr122 FF x xx). + exact (λ x y z xx yy zz f g ff gg, pr222 FF x y z f g xx yy zz ff gg). - exact (λ x, pr2 (pr1 FF x)). - intros x y xx yy f. exact (pr2 (pr12 FF x y xx yy f)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. 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.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq. Require Import UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId.