Definition is_binary_prod_enriched_to_BinProduct {a : enriched_binary_prod_cone} (Ha : is_binary_prod_enriched a) (w : C) : BinProduct V (E ⦃ w , x ⦄) (E ⦃ w , y ⦄). Proof. use make_BinProduct. - exact (E ⦃ w , a ⦄). - exact (postcomp_arr E w (enriched_prod_cone_pr1 a)). - exact (postcomp_arr E w (enriched_prod_cone_pr2 a)). - exact (Ha w). 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.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.Limits.BinProducts. Import MonoidalNotations. Section BinaryProductFromUnderlying. End BinaryProductFromUnderlying.