Definition span_associator_mor : comp_span_Pullback h₁ (comp_span h₂ h₃) --> comp_span_Pullback (comp_span h₁ h₂) h₃. Proof. use PullbackArrow. - use PullbackArrow. + exact (PullbackPr1 _). + exact (PullbackPr2 _ · PullbackPr1 _). + abstract (rewrite !assoc' ; rewrite PullbackSqrCommutes ; apply idpath). - exact (PullbackPr2 _ · PullbackPr2 _). - abstract (cbn ; rewrite !assoc ; rewrite PullbackArrow_PullbackPr2 ; rewrite !assoc' ; rewrite PullbackSqrCommutes ; apply idpath). Defined.
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.