Definition pair_2cell_pr2_alt {a₁ a₂ b₁ b₂ : B} {f₁ f₂ : a₁ --> b₁} {g₁ g₂ : a₂ --> b₂} (α : f₁ ==> f₂) (β : g₁ ==> g₂) : (α ⊗₂ β) ▹ π₂ • prod_1cell_pr2 (π₁ · f₂) (π₂ · g₂) = prod_1cell_pr2 (π₁ · f₁) (π₂ · g₁) • (π₂ ◃ β) := prod_2cell_pr2_alt (π₁ ◃ α) (π₂ ◃ β).
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.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. 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.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Univalence.