Definition enriched_conical_lim_from_prod_equalizers_mor : v --> E ⦃ w , lim ⦄. Proof. use (EqualizerIn (is_equalizer_enriched_to_Equalizer _ _ _ enriched_conical_lim_ob_from_prod_equalizers_is_equalizer w)). - exact (ProductArrow _ _ (is_prod_enriched_to_Product _ _ is_prod_src w) fs). - abstract (use (ProductArrow_eq _ _ _ (is_prod_enriched_to_Product _ _ is_prod_tar w)) ; intros ijk ; cbn ; pose (ProductPrCommutes I V _ (is_prod_enriched_to_Product E D is_prod_src w) _ fs) as p ; cbn in p ; rewrite !assoc' ; rewrite <- !postcomp_arr_comp ; rewrite enriched_conical_lim_from_prod_equalizers_l_pr ; rewrite enriched_conical_lim_from_prod_equalizers_r_pr ; rewrite postcomp_arr_comp ; rewrite !assoc ; rewrite !p ; refine (!_) ; apply qs). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers. Import MonoidalNotations.