proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Limits.Equalizers