Lemma folds_iso_equal : i = i'. Proof. apply folds_iso_eq. apply dirprodeq. - apply dirprodeq. + apply funextsec; intro. apply subtypePath. * intro. apply isapropisweq. * apply funextfun; intro f. eapply pathscomp0. { apply ϕ₁_is_comp. } symmetry. eapply pathscomp0. { apply ϕ₁_is_comp. } rewrite H. apply idpath. + apply funextsec; intro. apply subtypePath. * intro; apply isapropisweq. * apply funextfun. unfold homot. apply ϕ₂_determined. - apply subtypePath. { intro. apply isapropisweq. } apply funextfun. intro t. apply ϕo_determined. 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.