Definition total_set_category_pb_ump_1_mor_eq {x y : C₀} (f : x --> y) : pr1 (# G₁ (# P₁ f)) ((pr11 (αinv (P₁ x))) ((pr11 (# G₂ (pr1 (Hβ x)))) (pr2 (P₂ x)))) = pr1 (αinv (P₁ y)) (pr1 (# G₂ (pr1 (Hβ y))) (pr1 (# G₂ (pr1 (# P₂ f))) (pr2 (P₂ x)))).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.StreetOpFibration. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.GrothendieckConstruction.TotalCategory. Require Import UniMath.CategoryTheory.GrothendieckConstruction.Projection. Require Import UniMath.CategoryTheory.GrothendieckConstruction.IsosInTotal. Section PullbackFromTotal. End PullbackFromTotal.