fact: Definition is_precategory_one_assoc (C : precategory_data) : UU := ((∏ (a b : C) (f : a --> b), identity a · f = f) × (∏ (a b : C) (f : a --> b), f · identity b = f)) × (∏ (a b c d : C) (f : a --> b) (g : b --> c) (h : c --> d), f · (g · h) = (f · g) · h).
imports: UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Notations