Definition folds_id_comp_from_precat_data : folds_id_T := tpair (λ C : folds_ob_mor, (∏ a : C, a ⇒ a → hProp) × (∏ (a b c : C), (a ⇒ b) → (b ⇒ c) → (a ⇒ c) → hProp)) (pr1 C) (make_dirprod (@id_pred) (@comp_pred)).
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.Folds.folds_precat.