Lemma folds_iso_comp_prop : folds_iso_prop folds_iso_comp_data. Proof. repeat split. - intros. simpl. eapply weqcomp. + apply (pr1 (pr1 (pr1 (pr1 (pr2 i))))). + apply (pr1 (pr1 (pr1 (pr1 (pr2 i'))))). - intros; simpl; eapply weqcomp. + apply (pr2 (pr1 (pr1 (pr1 (pr2 i))))). + apply (pr2 (pr1 (pr1 (pr1 (pr2 i'))))). - intros; simpl; eapply weqcomp. + apply (pr2 (pr1 (pr1 (pr2 i)))). + apply (pr2 (pr1 (pr1 (pr2 i')))). - intros; simpl; eapply weqcomp. + apply (pr1 (pr1 (pr2 (pr1 (pr2 i))))). + apply (pr1 (pr1 (pr2 (pr1 (pr2 i'))))). - intros; simpl; eapply weqcomp. + apply (pr2 (pr1 (pr2 (pr1 (pr2 i))))). + apply (pr2 (pr1 (pr2 (pr1 (pr2 i'))))). - intros; simpl; eapply weqcomp. + apply (pr1 (pr2 (pr2 (pr1 (pr2 i))))). + apply (pr1 (pr2 (pr2 (pr1 (pr2 i'))))). - intros; simpl; eapply weqcomp. + apply (pr2 (pr2 (pr2 (pr1 (pr2 i))))). + apply (pr2 (pr2 (pr2 (pr1 (pr2 i'))))). - intros; simpl; eapply weqcomp. + apply (pr2 (pr2 i)). + apply (pr2 (pr2 i')). 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.