proposition: Lemma section_nat_trans_eq {C : category} {D : disp_cat C} (F F' : section_disp D) (a a' : section_nat_trans_disp 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'). apply proofirrelevance. apply isaprop_section_nat_trans_disp_axioms. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing