proposition: Proposition pr1_idtoiso_disp_functor {C₁ C₂ : category} {F : C₁ ⟶ C₂} {D₁ : disp_cat C₁} {D₂ : disp_cat C₂} (FF : disp_functor F D₁ D₂) {x : C₁} {xx yy : D₁ x} (p : xx = yy) : pr1 (idtoiso_disp (idpath (F x)) (maponpaths (FF x) p)) = transportf (λ z, _ -->[ z ] _) (functor_id F _) (♯FF (idtoiso_disp (idpath x) p)).
proof: Proof. induction p. cbn. 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