Proposition disp_functor_id_var {C₁ C₂ : category} {F : C₁ ⟶ C₂} {D₁ : disp_cat C₁} {D₂ : disp_cat C₂} (FF : disp_functor F D₁ D₂) {x : C₁} (xx : D₁ x) : id_disp (FF x xx) = transportf (λ z, _ -->[ z ] _) (functor_id F x) (♯ FF (id_disp xx)). Proof. rewrite disp_functor_id. rewrite transportfbinv. apply idpath. Qed.
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.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.