Definition struct_cospan_associator_mor : comp_struct_cospan_Pushout h₁ (comp_struct_cospan h₂ h₃) --> comp_struct_cospan_Pushout (comp_struct_cospan h₁ h₂) h₃. Proof. use PushoutArrow. - exact (PushoutIn1 _ · PushoutIn1 _). - use PushoutArrow. + exact (PushoutIn2 _ · PushoutIn1 _). + exact (PushoutIn2 _). + abstract (rewrite !assoc ; rewrite PushoutSqrCommutes ; apply idpath). - abstract (cbn ; rewrite !assoc' ; rewrite PushoutArrow_PushoutIn1 ; rewrite !assoc ; rewrite PushoutSqrCommutes ; 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.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.