Definition make_comp_cat_dependent_prod {C : comp_cat} (prd : ∏ (Γ : C) (A : ty Γ), dependent_product (cleaving_of_types C) (π A)) (stable : ∏ (Γ₁ Γ₂ : C) (A₁ : ty Γ₁) (A₂ : ty Γ₂) (s₁ : Γ₁ --> Γ₂) (s₂ : Γ₁ & A₁ --> Γ₂ & A₂) (p : s₂ · π A₂ = π A₁ · s₁) (Hp : isPullback p), right_beck_chevalley _ (π A₂) s₁ (π A₁) s₂ p (prd _ A₂) (prd _ A₁)) : comp_cat_dependent_prod C := prd ,, stable.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.LiftDispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.DFLCompCat. Require Import UniMath.Bicategories.ComprehensionCat.CompCatNotations.