Definition enriched_nat_trans_eq {A B : enriched_precat} {F G : enriched_functor A B} {a a' : enriched_nat_trans F G} : (∏ x : A, a x = a' x) -> a = a'. Proof. intro H. use total2_paths_b. - apply funextsec. assumption. - apply proofirrelevance. repeat (apply impred_isaprop; intro). apply homset_property. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Core.Isos. Import MonoidalNotations.