proposition: Proposition is_binary_coprod_enriched_arrow_eq {w : C} {f g : a --> w} (q₁ : enriched_coprod_cocone_in1 a · f = enriched_coprod_cocone_in1 a · g) (q₂ : enriched_coprod_cocone_in2 a · f = enriched_coprod_cocone_in2 a · g) : f = g.
proof: Proof. refine (!(enriched_to_from_arr E _) @ _ @ enriched_to_from_arr E _). apply maponpaths. use (BinProductArrowsEq _ _ _ (is_binary_coprod_enriched_to_BinProduct Ha w)). - cbn. unfold precomp_arr. rewrite !assoc. rewrite !tensor_rinvunitor. rewrite !assoc'. rewrite !(maponpaths (λ z, _ · z) (assoc _ _ _)). rewrite <- !tensor_split'. use (invmaponpathsweq (make_weq _ (isweq_enriched_to_arr E _ _))) ; cbn. rewrite !assoc. rewrite mon_rinvunitor_I_mon_linvunitor_I. rewrite <- !(enriched_to_arr_comp E). exact q₁. - cbn. unfold precomp_arr. rewrite !assoc. rewrite !tensor_rinvunitor. rewrite !assoc'. rewrite !(maponpaths (λ z, _ · z) (assoc _ _ _)). rewrite <- !tensor_split'. use (invmaponpathsweq (make_weq _ (isweq_enriched_to_arr E _ _))) ; cbn. rewrite !assoc. rewrite mon_rinvunitor_I_mon_linvunitor_I. rewrite <- !(enriched_to_arr_comp E). exact q₂. 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