Lemma lineator_is_nattrans_full (v1 v2 : V) (x1 x2 : C) (f : V⟦v1,v2⟧) (g : C⟦x1,x2⟧) : f ⊗^{ActD} # F g · ld v2 x2 = ld v1 x1 · # F (f ⊗^{ActC} g). Proof. intros. etrans. { unfold functoronmorphisms1. rewrite assoc'. rewrite lnl. apply assoc. } rewrite lnr. rewrite assoc'. apply maponpaths. apply pathsinv0, functor_comp. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.