proposition: Proposition precomp_postcomp_arr_assoc {C : category} {V : monoidal_cat} (E : enrichment C V) {w x y z : C} (f : x --> y) : (precomp_arr E z f #⊗ identity _) · enriched_comp E w x z = (identity _ #⊗ postcomp_arr E w f) · enriched_comp E _ _ _.
proof: Proof. unfold precomp_arr. rewrite !tensor_comp_id_r. rewrite !assoc'. rewrite enrichment_assoc. rewrite !assoc. apply maponpaths_2. unfold postcomp_arr. rewrite !tensor_comp_id_l. apply maponpaths_2. rewrite !assoc'. rewrite tensor_lassociator. rewrite !assoc. apply maponpaths_2. rewrite mon_inv_triangle. 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.covyoneda UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Monoidal.Categories