proposition: Proposition is_binary_coprod_enriched_arrow_in2 {w : C} (f : x --> w) (g : y --> w) : enriched_coprod_cocone_in2 a · is_binary_coprod_enriched_arrow f g = g.
proof: Proof. unfold is_binary_coprod_enriched_arrow, enriched_coprod_cocone_in2. use (invmaponpathsweq (make_weq _ (isweq_enriched_from_arr E _ _))) ; cbn. refine (_ @ BinProductPr2Commutes _ _ _ (is_binary_coprod_enriched_to_BinProduct Ha w) _ (enriched_from_arr E f) (enriched_from_arr E g)). cbn. unfold precomp_arr, enriched_coprod_cocone_in2. rewrite enriched_from_arr_comp. rewrite !assoc. apply maponpaths_2. rewrite !enriched_from_to_arr. rewrite tensor_rinvunitor. rewrite mon_linvunitor_I_mon_rinvunitor_I. rewrite !assoc'. apply maponpaths. rewrite <- tensor_split'. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts