Lemma ϕ₁_ϕ₂_are_inverse : is_inverse_in_precat (C:= C') (ϕ₁ i (id _ )) (ϕ₂ i (id _ )). Proof. split. - apply ϕ₁_ϕ₂_id. - apply ϕ₂_ϕ₁_id. 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.