proposition: Lemma folds_iso_equal : i = i'.
proof: 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.
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