Definition pb_1cell_on_comp_coh {a₁ a₂ a₃ b₁ b₂ : B} (f : b₁ --> b₂) {g₁ : a₁ --> b₂} {g₂ : a₂ --> b₂} {g₃ : a₃ --> b₂} {h₁ : a₁ --> a₂} {h₂ : a₂ --> a₃} (α : invertible_2cell g₁ (h₁ · g₂)) (β : invertible_2cell g₂ (h₂ · g₃)) : (pb_on_1cell_pr1 f α)^-1 • ((f /≃₁ α ◃ (pb_on_1cell_pr1 f β)^-1) • lassociator (f /≃₁ α) (f /≃₁ β) π₁) • (pb_1cell_on_comp f α β ▹ π₁) = (pb_on_1cell_pr1 f (comp_of_invertible_2cell α (comp_of_invertible_2cell (lwhisker_of_invertible_2cell h₁ β) (lassociator_invertible_2cell _ _ _)))) ^-1.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Limits.Pullbacks.