Definition strictify_unit_data_help3 (F : strict_psfunctor B₁ B₂) (X Y Z : B₁) (f : X --> Y) (g : Y --> Z) : ((id₁ ((pr111 F) X) ◃ psfunctor_comp (strict_psfunctor_to_psfunctor_map B₁ B₂ F) f g) • lunitor (# F (f · g))) • rinvunitor (# F (f · g)) = (lassociator (id₁ ((pr111 F) X)) (# F f) (# F g)) • ((lunitor (# F f) • rinvunitor (# F f)) ▹ # F g) • rassociator (#F f) (id₁ (F Y)) (# F g) • (# F f ◃ (lunitor (# F g) • rinvunitor (# F g))) • lassociator (#F f) (#F g) (id₁ ((pr111 F) Z)) • (idtoiso_2_1 ((pr222 (pr1 F)) X Y Z f g) ▹ id₁ ((pr111 F) Z)).
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.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.StrictPseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.Base. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map1Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map2Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.StrictIdentitor. Require Import UniMath.Bicategories.PseudoFunctors.Display.StrictCompositor. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.StrictPseudoFunctor. Import PseudoFunctor.Notations. Import StrictPseudoFunctor.Notations. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.PseudoFunctors.Examples.StrictToPseudo. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition.