proposition: Lemma disp_functor_idtoiso_twosided_disp {x y : C} (xx := x ,, y : category_binproduct C C) {xy₁ xy₂ : D₁ x y} (p : xy₁ = xy₂) (f := idtoiso_twosided_disp (idpath x) (idpath y) p : xy₁ -->[ identity _ ][ identity _ ] xy₂) (φ := f : @mor_disp _ (twosided_disp_cat_to_disp_cat C C D₁) xx xx xy₁ xy₂ (identity _ ,, identity _)) (ψ := idtoiso_twosided_disp (idpath _) (idpath _) (maponpaths (F xx) p) : F xx xy₁ -->[ identity _ ][ identity _ ] F xx xy₂) : (♯F φ = ψ)%mor_disp.
proof: Proof. induction p ; cbn. exact (disp_functor_id F (x := xx) xy₁). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq UniMath.CategoryTheory.DisplayedCats.Examples.DispFunctorPair UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws