Proposition is_z_iso_span_runitor_mor_eqs : is_inverse_in_precat span_runitor_mor span_rinvunitor. Proof. split ; unfold span_runitor_mor, span_rinvunitor ; cbn. - use (MorphismsIntoPullbackEqual (isPullback_Pullback (PC _ _ _ _ _))) ; cbn. + rewrite !assoc'. rewrite PullbackArrow_PullbackPr1. rewrite id_left. apply id_right. + rewrite !assoc'. rewrite PullbackArrow_PullbackPr2. rewrite id_left. rewrite PullbackSqrCommutes. apply id_right. - apply PullbackArrow_PullbackPr1. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Constant. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.DispCatOnTwoSidedDispCat.