Definition is_coprod_enriched_from_iso : is_coprod_enriched enriched_coprod_cocone_from_iso. Proof. intros w. use (isProduct_z_iso _ _ _ _ (Ha w)). - exact (precomp_arr_z_iso E w f). - abstract (intro j ; cbn ; rewrite <- precomp_arr_comp ; apply maponpaths ; unfold enriched_coprod_cocone_from_iso ; cbn ; unfold enriched_coprod_cocone_in ; cbn ; rewrite enriched_to_from_arr ; apply idpath). 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.Products. Require Import UniMath.CategoryTheory.Limits.Coproducts. Import MonoidalNotations. Section CoproductFromUnderlying. End CoproductFromUnderlying.