proposition: 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: Proof. unfold preserve_ptset. unfold funcomp. etrans. { apply maponpaths. apply pf. } apply pg. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Binproducts UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Examples.DisplayedCartesianMonoidal UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal