proposition: Proposition Kleisli_cat_enrichment_postcomp_arr {x y : Kleisli_cat_monad M} (w : Kleisli_cat_monad M) (f : x --> y) : postcomp_arr Kleisli_cat_monad_enrichment w f = postcomp_arr E w (#M f · μ M y).
proof: Proof. unfold postcomp_arr ; cbn. rewrite !assoc'. apply maponpaths. rewrite enriched_comp_postcomp_arr. rewrite !assoc. apply maponpaths_2. rewrite <- !tensor_comp_id_r. apply maponpaths_2. rewrite <- functor_enrichment_from_arr. rewrite enriched_from_arr_postcomp. 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.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.EnrichedCats.EnrichmentMonad UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.KleisliCategory