Proposition comp_struct_cospan_mor_laws : struct_cospan_laws L v₁ v₃ (comp_struct_cospan h₁ h₂) (comp_struct_cospan k₁ k₂) mor_of_comp_struct_cospan_mor. Proof. split ; cbn. - unfold mor_of_comp_struct_cospan_mor. rewrite !assoc'. rewrite PushoutArrow_PushoutIn1. rewrite !assoc. apply maponpaths_2. apply struct_cospan_sqr_mor_left. - unfold mor_of_comp_struct_cospan_mor. rewrite !assoc'. rewrite PushoutArrow_PushoutIn2. rewrite !assoc. apply maponpaths_2. apply struct_cospan_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.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.