Definition inserter_conservative_inv : g₂ ==> g₁. Proof. use (inserter_ump_cell H). - exact (Hβ^-1). - abstract (cbn ; use vcomp_move_R_Mp ; [ is_iso | ] ; cbn ; rewrite !vassocl ; rewrite rwhisker_rwhisker ; use vcomp_move_L_pM ; [ is_iso | ] ; cbn ; rewrite !vassocr ; apply maponpaths_2 ; rewrite rwhisker_rwhisker_alt ; rewrite !vassocl ; apply maponpaths ; rewrite vcomp_whisker ; apply idpath). Defined.
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.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms.