Lemma comp_preserve_ptset {X Y Z : hSet} {x : X} {y : Y} {z : Z} {f : X → Y} {g : Y→ Z} (pf : preserve_ptset x y f) (pg : preserve_ptset y z g) : preserve_ptset x z (funcomp f g). Proof. unfold preserve_ptset. unfold funcomp. etrans. { apply maponpaths. apply pf. } apply pg. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.DisplayedCartesianMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal. Import DisplayedBifunctorNotations.