proposition: Proposition enriched_conical_lim_eq_from_prod_equalizers {i j : I} (k : i --> j) : enriched_conical_lim_pr_from_prod_equalizers i · # D k = enriched_conical_lim_pr_from_prod_equalizers j.
proof: Proof. unfold enriched_conical_lim_pr_from_prod_equalizers. rewrite !assoc'. rewrite <- enriched_conical_lim_from_prod_equalizers_r_pr. rewrite <- (enriched_conical_lim_from_prod_equalizers_l_pr k). rewrite !assoc. apply maponpaths_2. refine (!_). exact (enriched_equalizer_cone_eq _ _ _ (pr1 (EE _ _ f g))). 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