proposition: Lemma DH0_DH1_nat_trans_axioms {DH0 DH1 :disp_functor H D' D''} (β: disp_nat_trans (nat_z_iso_id (F ∙ H)) (DF ◦ DH0) (DF ◦ DH1)) : disp_nat_trans_axioms (DH0_DH1_nat_trans_data β).
proof: Proof. intros a' b' f' x' y' Df'. induction x' as (a,(px,x)). induction y' as (b,(py,y)). induction Df' as (f,(pf,Df)). destruct px, py, pf. cbn. etrans. apply (pr2 β a b f x y Df). apply two_arg_paths. - apply uip. apply homset_property. - reflexivity. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.StreetFibration