proposition: Proposition internal_pre_post_comp_as_pre_post_comp {x₁ x₂ : V} (f : x₁ --> x₂) {y₁ y₂ : V} (g : y₁ --> y₂) : internal_pre_post_comp f g = internal_precomp f y₁ · internal_postcomp x₁ g.
proof: Proof. use internal_funext. intros a h. rewrite tensor_split. rewrite tensor_comp_r_id_r. rewrite !assoc'. unfold internal_precomp, internal_postcomp, internal_pre_post_comp. rewrite !internal_beta. refine (!_). rewrite tensor_split. rewrite !assoc'. apply maponpaths. rewrite !assoc. rewrite internal_beta. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric