Lemma idtoiso_2_1_concat {C : bicat} {a b : C} {f₁ f₂ f₃ : a --> b} (p : f₁ = f₂) (q : f₂ = f₃) : idtoiso_2_1 _ _ (p @ q) = comp_of_invertible_2cell (idtoiso_2_1 _ _ p) (idtoiso_2_1 _ _ q). Proof. induction p ; induction q ; cbn. use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } exact (!(id2_left _)). 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.