proposition: Proposition is_conical_colim_enriched_arrow_eq {w : C} {f g : a --> w} (q : ∏ (i : I), enriched_conical_colim_cocone_in a i · f = enriched_conical_colim_cocone_in a i · g) : f = g.
proof: Proof. refine (!(enriched_to_from_arr E _) @ _ @ enriched_to_from_arr E _). apply maponpaths. use (arr_to_LimCone_eq (is_conical_colim_enriched_to_Lim (pr2 a) w)). intro i ; cbn. rewrite !enriched_from_arr_precomp. rewrite q. 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.OppositeCategory.Core UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoequalizers