Lemma ϕ₁_ϕ₂_id : ϕ₁ i (id _ ) □ (ϕ₂ i (id _ )) = id _. Proof. set (q:=pr2 (pr1 (pr1 (pr1 (pr2 i))))). simpl in q. specialize (q _ _ (id _ ) (id _ ) (id _ )). set (q':=pr1 q ); clearbody q'. apply comp_compose2'. apply q'. 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.