Definition make_disp_pstrans {F₁ F₂ : psfunctor B₁ B₂} {FF₁ : disp_psfunctor D₁ D₂ F₁} {FF₂ : disp_psfunctor D₁ D₂ F₂} {α : pstrans F₁ F₂} (αα₁ : ∏ (x : B₁) (xx : D₁ x), FF₁ x xx -->[ α x] FF₂ x xx) (αα₂ : ∏ (x y : B₁) (f : B₁ ⟦ x, y ⟧) (xx : D₁ x) (yy : D₁ y) (ff : xx -->[ f] yy), (αα₁ x xx;; disp_psfunctor_mor D₁ D₂ F₂ FF₂ ff) ==>[ psnaturality_of α f ] disp_psfunctor_mor D₁ D₂ F₁ FF₁ ff;; αα₁ y yy) : disp_pstrans FF₁ FF₂ α. Proof. use tpair. - use make_disp_pstrans_data. + exact αα₁. + intros. use tpair. * apply αα₂. * apply HD₂. - abstract (repeat split; intro; intros; apply HD₁). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispTransformation. Require Import UniMath.Bicategories.DisplayedBicats.DispModification.