Definition make_is_equalizer_enriched_from_z_iso (EqV : Equalizers V) (a : enriched_equalizer_cone) (Ha : ∏ (w : C), is_z_isomorphism (equalizer_enriched_to_equalizer EqV a w)) : is_equalizer_enriched a. Proof. intro w. use (isEqualizer_z_iso (pr22 (EqV (E ⦃ w, x ⦄) (E ⦃ w, y ⦄) (postcomp_arr E w f) (postcomp_arr E w g))) (_ ,, Ha w)). abstract (unfold equalizer_enriched_to_equalizer ; cbn ; refine (!_) ; apply EqualizerCommutes). 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.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.Limits.Equalizers. Import MonoidalNotations. Section EqualizersFromUnderlying. End EqualizersFromUnderlying.