proposition: Proposition enriched_conical_lim_from_prod_equalizers_commute (i : I) : enriched_conical_lim_from_prod_equalizers_mor · postcomp_arr E w (enriched_conical_lim_pr_from_prod_equalizers i) = fs i.
proof: Proof. unfold enriched_conical_lim_from_prod_equalizers_mor. unfold enriched_conical_lim_pr_from_prod_equalizers. rewrite postcomp_arr_comp. rewrite !assoc. rewrite (EqualizerCommutes (is_equalizer_enriched_to_Equalizer E f g enriched_conical_lim_ob_from_prod_equalizers_is_equalizer w)). rewrite (ProductPrCommutes _ _ _ (is_prod_enriched_to_Product E D is_prod_src w)). 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.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.Limits.EnrichedProducts UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers