Definition disp_nat_trans_comp {C' C : category} {F'' F' F : functor_data C' C} {a' : nat_trans F'' F'} {a : nat_trans F' F} {D' : disp_cat_data C'} {D : disp_cat C} {R'' : disp_functor_data F'' D' D} {R' : disp_functor_data F' D' D} {R : disp_functor_data F D' D} (b' : disp_nat_trans a' R'' R') (b : disp_nat_trans a R' R) : disp_nat_trans (nat_trans_comp _ _ _ a' a) R'' R. Proof. use tpair. - intros x xx. apply (comp_disp (b' _ _ ) (b _ _ )). - apply disp_nat_trans_comp_ax. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.