Definition product_enrichment_pr2_comp (x₁ y₁ z₁ : C₁) (x₂ y₂ z₂ : C₂) : product_enrichment_hom y₁ z₁ y₂ z₂ ⊗ product_enrichment_hom x₁ y₁ x₂ y₂ --> (E₂ ⦃ y₂, z₂ ⦄) ⊗ (E₂ ⦃ x₂, y₂ ⦄). Proof. use (BinProductArrow _ (is_cartesian_BinProduct HV _ _)). - exact (semi_cart_tensor_pr1 HV _ _ · semi_cart_tensor_pr2 HV _ _). - exact (semi_cart_tensor_pr2 HV _ _ · semi_cart_tensor_pr2 HV _ _). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Import MonoidalNotations.