Lemma disp_functor_transportf_disp_mor2 {x₁ x₂ y₁ y₂ : C} (xx := (x₁ ,, y₁) : category_binproduct C C) (yy := (x₂ ,, y₂) : category_binproduct C C) {f f' : x₁ --> x₂} {g g' : y₁ --> y₂} (p : f = f') (q : g = g') {xy₁ : D₁ x₁ y₁} {xy₂ : D₁ x₂ y₂} (fg : xy₁ -->[ f ][ g ] xy₂) (fg' := fg : @mor_disp _ (twosided_disp_cat_to_disp_cat C C D₁) xx yy xy₁ xy₂ (f ,, g)) (φ := transportf_disp_mor2 p q fg' : @mor_disp _ (twosided_disp_cat_to_disp_cat C C D₁) xx yy xy₁ xy₂ (f' ,, g')) : (♯F φ = transportf_disp_mor2 p q (♯F fg'))%mor_disp. Proof. induction p, q. refine (!_). apply transportf_disp_mor2_idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.DispFunctorPair. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Section FromIso. End FromIso.