proposition: Lemma nat_trans_eq {C C' : precategory_data} (hs: has_homsets C') (F F' : functor_data C C')(a a' : nat_trans F F'): (∏ x, a x = a' x) -> a = a'.
proof: Proof. intro H. assert (H' : pr1 a = pr1 a'). { now apply funextsec. } apply (total2_paths_f H'), proofirrelevance, isaprop_is_nat_trans, hs. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence