fact: Definition prebicategory_id_comp := ∑ C : prebicategory_ob_hom, (∏ a : C, a -1-> a) × (∏ a b c : C, ((a -1-> b) c× (b -1-> c)) ⟶ (a -1-> c)).
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.Equivalences.Core