Definition id1_conservative {B : bicat} (a : B) : conservative_1cell (id₁ a). Proof. intros x g₁ g₂ α Hα. pose ((α ▹ id₁ a) • runitor _). use eq_is_invertible_2cell. - exact (rinvunitor _ • (α ▹ id₁ _) • runitor _). - rewrite !vassocl. rewrite vcomp_runitor. rewrite !vassocr. rewrite !rinvunitor_runitor. apply id2_left. - use is_invertible_2cell_vcomp. + use is_invertible_2cell_vcomp. * apply is_invertible_2cell_rinvunitor. * exact Hα. + apply is_invertible_2cell_runitor. 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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration.