Definition transportf_struct_mor_prod_via_transportf {X₁ X₂ X₃ Y₁ Y₂ Y₃ : hSet} (p₁ : X₁ = Y₁) (PX₁ : P X₁) (p₂ : X₂ = Y₂) (PX₂ : P X₂) (p₃ : X₃ = Y₃) (PX₃ : P X₃) (f : X₁ × X₂ → X₃) (Hf : mor_hset_struct P (hset_struct_prod P PX₁ PX₂) PX₃ f) : mor_hset_struct P (hset_struct_prod P (transportf P p₁ PX₁) (transportf P p₂ PX₂)) (transportf P p₃ PX₃) (transportf_mor_weq_prod (hSet_univalence_map _ _ p₁) (hSet_univalence_map _ _ p₂) (hSet_univalence_map _ _ p₃) f).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts.