proposition: Lemma disp_nat_trans_ax_var {C' C : precategory_data} {F' F : functor_data C' C} {a : nat_trans F' F} {D' : disp_cat_data C'} {D : disp_cat_data C} {R' : disp_functor_data F' D' D} {R : disp_functor_data F D' D} (b : disp_nat_trans a R' R) {x' x : C'} {f : x' --> x} {xx' : D' x'} {xx : D' x} (ff : xx' -->[ f ] xx): b _ xx' ;; ♯ R ff = transportf _ (nat_trans_ax a _ _ f) (♯ R' ff ;; b _ xx).
proof: Proof. apply pathsinv0, transportf_pathsinv0. apply pathsinv0, disp_nat_trans_ax. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Isos