Definition inserter_ump_1_slice_mor_inv2cell : invertible_2cell (pr21 q) (inserter_ump_1_slice_mor_to_eq · (p' · p · pr2 h₁)). Proof. use make_invertible_2cell. - exact (pr12 (inserter_cone_pr1 q) • ((inserter_ump_mor_pr1 HI _ _)^-1 ▹ _) • ((equifier_ump_mor_pr1 HE _ _)^-1 ▹ _ ▹ _) • (rassociator _ _ _ ▹ _) • rassociator _ _ _). - is_iso. apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. 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.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Inserters. Require Import UniMath.Bicategories.Limits.Equifiers.