proposition: Lemma folds_iso_comp_prop : folds_iso_prop folds_iso_comp_data.
proof: 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.
imports: UniMath.Folds.UnicodeNotations UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.Folds.folds_precat UniMath.Folds.from_precats_to_folds_and_back