proposition: 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: Proof. rewrite disp_functor_id. rewrite transportfbinv. apply idpath. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos