proposition: Proposition self_enrichment_postcomp {w x y : V} (f : x --> y) : postcomp_arr self_enrichment w f = internal_lam (internal_eval _ _ · f).
proof: Proof. use internal_funext. intros a h. unfold postcomp_arr ; cbn. rewrite !tensor_comp_r_id_r. etrans. { rewrite !assoc'. unfold internal_comp. rewrite !internal_beta. etrans. { apply maponpaths. rewrite !assoc. rewrite tensor_lassociator. rewrite !assoc'. apply maponpaths. rewrite tensor_id_id. rewrite !assoc. rewrite <- tensor_split'. rewrite tensor_split. rewrite !assoc'. unfold internal_from_arr. rewrite internal_beta. rewrite !assoc. rewrite tensor_lunitor. apply idpath. } etrans. { apply maponpaths. rewrite !assoc. rewrite mon_lunitor_triangle. apply idpath. } rewrite !assoc. rewrite <- tensor_comp_mor. rewrite id_right. rewrite mon_linvunitor_lunitor. apply idpath. } refine (!_). etrans. { rewrite tensor_split. rewrite !assoc'. rewrite internal_beta. apply idpath. } rewrite !assoc. 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.Monads.Monads UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.EnrichedCats.EnrichmentMonad UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.StrongMonad UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed