Lemma pointedtensorialstrength_lineator_nat_left {C : category} (M : monoidal C) {F : functor C C} (pts : pointedtensorialstrength M F): lineator_nat_left _ _ _ _ pts = ∏ (v : coslice_cat_total C I_{M}) (x1 x2 : C) (g : C⟦x1,x2⟧), pr1 v ⊗^{ M}_{l} # F g · pts v x2 = pts v x1 · # F (pr1 v ⊗^{ M}_{l} g). Proof. apply idpath. 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.