Definition E_is_good_to_I_and_T (C : folds_3_id_comp_eq) : UU := (((∏ (a b : C) (f : a ⇒ b), E f f) × (∏ (a b : C) (f g : a ⇒ b), E f g → E g f)) × (∏ (a b : C) (f g h : a ⇒ b), E f g → E g h → E f h)) × ((∏ (a : C) (f g : a ⇒ a), E f g → I f → I g) × (∏ (a b c : C) (f f' : a ⇒ b) (g g' : b ⇒ c) (h h' : a ⇒ c), E f f' → E g g' → E h h' → T f g h → T f' g' h')).
Require Import UniMath.Folds.UnicodeNotations. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets.