Lemma disp_binprod_transportf_pr1 (a b : C) (f g : a --> b) (a' b' : C') (f' g' : a' --> b') (x : D a) (y : D b) (x' : D' a') (y' : D' b') (ff : x -->[f] y) (ff' : x' -->[f'] y') (e : catbinprodmor f f' = catbinprodmor g g') : transportf (mor_disp _ _) (maponpaths pr1 e) ff = pr1 (transportf (@mor_disp _ disp_binprod_data (a,,a') _ (x,, x') (_,, _)) e (ff,, ff')) . Proof. induction e. apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.