proposition: Proposition is_binary_prod_enriched_arrow_pr2 {w : C} (f : w --> x) (g : w --> y) : is_binary_prod_enriched_arrow f g · enriched_prod_cone_pr2 a = g.
proof: Proof. unfold is_binary_prod_enriched_arrow, enriched_prod_cone_pr2. use (invmaponpathsweq (make_weq _ (isweq_enriched_from_arr E _ _))) ; cbn. refine (_ @ BinProductPr2Commutes _ _ _ (is_binary_prod_enriched_to_BinProduct Ha w) _ (enriched_from_arr E f) (enriched_from_arr E g)). cbn. unfold postcomp_arr, enriched_prod_cone_pr2. rewrite enriched_from_arr_comp. rewrite !assoc. apply maponpaths_2. rewrite tensor_linvunitor. rewrite !assoc'. apply maponpaths. rewrite <- tensor_split. rewrite !enriched_from_to_arr. 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