Definition disp_cat_eq_step_3 : pr1 D₁ ╝ pr1 D₂ ≃ ∑ (p : pr11 D₁ ╝ pr11 D₂), transportf (disp_cat_id_comp C) (total2_paths_f (pr1 p) (pr2 p)) (pr21 D₁) = pr21 D₂. Proof. exact (invweq (weqfp (invweq (total2_paths_equiv _ (pr11 D₁) (pr11 D₂))) (λ p, transportf _ p (pr21 D₁) = pr21 D₂))). 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.