Corollary associativity_pentagon {a b c d e : C} (f : C ⟦ a, b ⟧) (g : C ⟦ b, c ⟧) (h : C ⟦ c, d ⟧) (i : C ⟦ d, e ⟧) : (rassociator f g h ⋆ id2 i • rassociator f (g · h) i) • id2 f ⋆ rassociator g h i = rassociator (f · g) h i • rassociator f g (h · i). Proof. unfold hcomp. rewrite id2_rwhisker. rewrite lwhisker_id2. rewrite id2_right. rewrite id2_left. apply rassociator_rassociator. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.