Definition transportf_disp_map_bicat_cell {y₁ y₂ : B} {g₁ g₂ : y₁ --> y₂} {β₁ β₂ : g₁ ==> g₂} (p : β₁ = β₂) {h₁ : disp_map_bicat_ob y₁} {h₂ : disp_map_bicat_ob y₂} {f₁ : disp_map_bicat_mor h₁ h₂ g₁} {f₂ : disp_map_bicat_mor h₁ h₂ g₂} (γ : disp_map_bicat_cell f₁ f₂ β₁) : pr1 (transportf (λ α, disp_map_bicat_cell f₁ f₂ α) p γ) = pr1 γ.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.Limits.Pullbacks.