Definition mor_of_comp_struct_cospan_mor : comp_struct_cospan_Pushout h₁ h₂ --> comp_struct_cospan_Pushout k₁ k₂. Proof. use PushoutArrow. - exact (struct_cospan_sqr_ob_mor _ s₁ · PushoutIn1 _). - exact (struct_cospan_sqr_ob_mor _ s₂ · PushoutIn2 _). - abstract (rewrite !assoc ; rewrite struct_cospan_sqr_mor_right ; rewrite struct_cospan_sqr_mor_left ; rewrite !assoc' ; apply maponpaths ; apply PushoutSqrCommutes). 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. 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.