Lemma independent_transportation_commutes {C : univalent_category} {F G : C -> C -> C} {x1 x2 y1 y2 : C} (p1 : F x1 y1 = G x1 y1) (p2 : F x2 y2 = G x2 y2) (f : C⟦F x1 y1, F x2 y2⟧) : transportf (λ c : C, C ⟦ G x1 y1, c ⟧) p2 (transportf (λ c : C, C ⟦ c, F x2 y2 ⟧) p1 f) = transportf (λ c : C, C ⟦ c, G x2 y2 ⟧) p1 (transportf (λ c : C, C ⟦ F x1 y1, c ⟧) p2 f). Proof. induction p1 ; induction p2. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Import TensorNotation. Import TensorNotation.