fact: Definition folds_pre_3_cat := ∑ C : folds_3_id_comp_eq, (folds_ax_id C × folds_ax_comp C) × E_is_good_to_I_and_T C.
imports: UniMath.Folds.UnicodeNotations UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets