fact: Definition nat_trans_total_category_of_set_functor_eq (x : total_precategory_of_set_functor G₁) : pr1 (# G₂ (α (pr1 x))) (pr1 (pr1 β₁ (pr1 x)) (pr2 x)) = pr1 (pr1 β₂ (pr1 x)) (pr2 x).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.GrothendieckConstruction.TotalCategory