Lemma isotoid_2_1_lwhisker {B : bicat} (HB : is_univalent_2_1 B) {a b c : B} (f : a --> b) {g₁ g₂ : b --> c} (α : invertible_2cell g₁ g₂) : maponpaths (λ z : b --> c, f · z) (isotoid_2_1 HB α) = isotoid_2_1 HB (f ◃ α ,, is_invertible_2cell_lwhisker _ (pr2 α)). Proof. use (invmaponpathsincl (idtoiso_2_1 _ _)). - apply isinclweq. exact (HB _ _ _ _). - use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } etrans. { refine (!_). apply idtoiso_2_1_lwhisker. } rewrite !idtoiso_2_1_isotoid_2_1. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.