Lemma isotoid_2_1_vcomp {B : bicat} (HB : is_univalent_2_1 B) {a b : B} {f₁ f₂ f₃ : a --> b} (α : invertible_2cell f₁ f₂) (β : invertible_2cell f₂ f₃) : isotoid_2_1 HB α @ isotoid_2_1 HB β = isotoid_2_1 HB (α • β ,, is_invertible_2cell_vcomp (pr2 α) (pr2 β)). Proof. use (invmaponpathsincl (idtoiso_2_1 _ _)). - apply isinclweq. exact (HB _ _ _ _). - etrans. { apply idtoiso_2_1_concat. } use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } 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.