Definition transportf_struct_mor_prod_via_eq {X₁ X₂ X₃ Y₁ Y₂ Y₃ : hSet} (w₁ : X₁ ≃ Y₁) (PX₁ : P X₁) (w₂ : X₂ ≃ Y₂) (PX₂ : P X₂) (w₃ : X₃ ≃ Y₃) (PX₃ : P X₃) (f : X₁ × X₂ → X₃) (Hf : mor_hset_struct P (hset_struct_prod P PX₁ PX₂) PX₃ f) (g : Y₁ × Y₂ → Y₃) (p : ∏ (y : Y₁ × Y₂), g y = transportf_mor_weq_prod w₁ w₂ w₃ f y) : mor_hset_struct P (hset_struct_prod P (transportf_struct_weq P w₁ PX₁) (transportf_struct_weq P w₂ PX₂)) (transportf_struct_weq P w₃ PX₃) g.
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.