Definition strict_counit_data_help (F G : psfunctor B₁ B₂) (α : pstrans F G) (X Y : B₁) (f : X --> Y) : (rassociator (id₁ (F X)) ((pr111 α) X) (#G f)) • (id₁ (F X) ◃ (psnaturality_of α f)) • (lassociator (id₁ (F X)) (#F f) (α Y)) • (((lunitor (# F f) • rinvunitor (# F f)) ▹ α Y)) • (rassociator (# F f) (id₁ (F Y)) (α Y)) • (# F f ◃ (lunitor (α Y) • rinvunitor (α Y))) = ((lunitor ((pr111 α) X) • rinvunitor (α X)) ▹ # G f) • (rassociator (α X) (id₁ (G X)) (# G f)) • ((α X ◃ (lunitor (# G f) • rinvunitor (# G f)))) • (lassociator (α X) (# G f) (id₁ (G Y))) • ((psnaturality_of α f ▹ id₁ (G Y))) • rassociator (# F f) (α Y) (id₁ (G Y)).
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.