Definition cod_1cell_path_help {B : bicat} {b c : B} (f₁ f₂ : B ⟦ b , c ⟧) : invertible_2cell f₁ f₂ ≃ invertible_2cell f₁ (id₁ _ · f₂). Proof. use make_weq. - intro α. refine (α • linvunitor _ ,, _). is_iso. apply α. - use isweq_iso. + intro α. use make_invertible_2cell. * exact (α • lunitor _). * is_iso. apply property_from_invertible_2cell. + abstract (intro p ; use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; cbn ; rewrite vassocl ; rewrite linvunitor_lunitor ; apply id2_right). + abstract (intros α ; cbn ; use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; cbn ; rewrite vassocl ; rewrite lunitor_linvunitor ; apply id2_right). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.OneTypes. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Trivial. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma.