Definition identity_internal_cleaving : internal_sfib_cleaving (id₁ b). Proof. intros x f g α. refine (f ,, α • runitor _ ,, runitor_invertible_2cell _ ,, _ ,, _) ; cbn. - apply identity_is_cartesian_2cell_sfib. - abstract (rewrite <- vcomp_runitor ; rewrite <- rwhisker_vcomp ; apply maponpaths ; rewrite <- runitor_triangle ; use vcomp_move_L_pM ; [ is_iso | ] ; cbn ; rewrite runitor_rwhisker ; rewrite lunitor_runitor_identity ; 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.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.