Proposition comp_span_mor_laws : span_laws v₁ v₃ (comp_span h₁ h₂) (comp_span k₁ k₂) mor_of_comp_span_mor. Proof. split ; cbn. - unfold mor_of_comp_span_mor. rewrite !assoc. rewrite PullbackArrow_PullbackPr1. rewrite !assoc'. apply maponpaths. apply span_sqr_mor_left. - unfold mor_of_comp_span_mor. rewrite !assoc. rewrite PullbackArrow_PullbackPr2. rewrite !assoc'. apply maponpaths. apply span_sqr_mor_right. 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.