Proposition isaprop_preserves_dependent_sums {C₁ C₂ : category} {D₁ : disp_cat C₁} {HD₁ : cleaving D₁} {D₂ : disp_cat C₂} {HD₂ : cleaving D₂} {F : C₁ ⟶ C₂} (FF : cartesian_disp_functor F D₁ D₂) (L₁ : has_dependent_sums HD₁) (L₂ : has_dependent_sums HD₂) : isaprop (preserves_dependent_sums FF L₁ L₂). Proof. do 4 (use impred ; intro). apply isaprop_is_z_isomorphism. Qed.
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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Pullbacks.