Lemma triangle_identity {a b c : C} (f : C ⟦ a, b ⟧) (g : C ⟦ b, c ⟧) : id2 f ⋆ lunitor g = lassociator f (identity b) g • (runitor f ⋆ id2 g). Proof. unfold hcomp at 2. rewrite vassocr. rewrite runitor_rwhisker. rewrite hcomp_hcomp'. unfold hcomp'. apply maponpaths. rewrite lwhisker_id2. apply id2_rwhisker. 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.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.WkCatEnrichment.Notations. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.