Lemma ϕ₂_ϕ₁_id: ϕ₂ i (id a) □ ϕ₁ i (id a) = id b. Proof. set (H':= pr2 (pr1 (pr2 (pr1 (pr2 i))))). simpl in H'. specialize (H' _ (id _ ) (id _ ) (id _ )). simpl in H'. rewrite <- ϕo_id. apply comp_compose2'. apply H'. apply comp_compose2. apply T_I_l. Qed.
Require Import UniMath.Folds.UnicodeNotations. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.Folds.folds_precat. Require Import UniMath.Folds.from_precats_to_folds_and_back.