Definition Equalizer_z_iso_lr : Equalizer f₂ g₂. Proof. use make_Equalizer. - exact E. - exact ι. - exact Equalizer_z_iso_lr_eq. - intros w h s. use iscontraprop1. + exact (Equalizer_z_iso_lr_unique h). + simple refine (EqualizerIn E w (h · l) _ ,, _). * abstract (rewrite !assoc' ; rewrite p, q ; rewrite !assoc ; rewrite s ; apply idpath). * abstract (cbn ; unfold ι ; rewrite !assoc ; rewrite EqualizerCommutes ; rewrite !assoc' ; rewrite z_iso_inv_after_z_iso ; apply id_right). 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.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.BinCoproducts.