Definition right_biadj_preserves_equifiers_nat_trans_cell {x : B₁} (h : x --> R e) : biadj_unit R x · # R (# L h · biadj_counit R e · equifier_cone_pr1 e) ==> h · # R (equifier_cone_pr1 e) := (_ ◃ ((psfunctor_comp R _ _)^-1 • ((psfunctor_comp R _ _)^-1 ▹ _))) • lassociator _ _ _ • (lassociator _ _ _ ▹ _) • (((psnaturality_of (biadj_unit R) h) ▹ _) ▹ _) • rassociator _ _ _ • rassociator _ _ _ • (_ ◃ (lassociator _ _ _ • ((linvunitor _ • (_ ◃ (_ ◃ (linvunitor _ • (_ ◃ rinvunitor _)))) • invertible_modcomponent_of (biadj_triangle_r R) e) ▹ _) • lunitor _)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Subcategory.FullEquivalences. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Properties. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderInvertibles. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.PseudoFunctors.Preservation.Preservation. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.Limits.Equifiers.