Proposition dialgebra_enrichment_precomp_arr {f g : dialgebra F G} (h : dialgebra F G) (τ : f --> g) : precomp_arr dialgebra_enrichment h τ · dialgebra_enrichment_mor_incl _ _ = dialgebra_enrichment_mor_incl _ _ · precomp_arr _ _ (pr1 τ). Proof. unfold precomp_arr. cbn. rewrite !assoc'. rewrite dialgebra_enrichment_comp_incl. unfold dialgebra_enrichment_comp_mor. rewrite !assoc. apply maponpaths_2. rewrite !assoc'. rewrite <- tensor_comp_mor. rewrite id_left. rewrite dialgebra_enrichment_from_arr_incl. rewrite tensor_split'. rewrite !assoc. apply maponpaths_2. rewrite tensor_rinvunitor. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Limits.Equalizers. Import MonoidalNotations.