proposition: Lemma disp_functor_transportf_disp_mor2 {x₁ x₂ y₁ y₂ : C} (xx := (x₁ ,, y₁) : category_binproduct C C) (yy := (x₂ ,, y₂) : category_binproduct C C) {f f' : x₁ --> x₂} {g g' : y₁ --> y₂} (p : f = f') (q : g = g') {xy₁ : D₁ x₁ y₁} {xy₂ : D₁ x₂ y₂} (fg : xy₁ -->[ f ][ g ] xy₂) (fg' := fg : @mor_disp _ (twosided_disp_cat_to_disp_cat C C D₁) xx yy xy₁ xy₂ (f ,, g)) (φ := transportf_disp_mor2 p q fg' : @mor_disp _ (twosided_disp_cat_to_disp_cat C C D₁) xx yy xy₁ xy₂ (f' ,, g')) : (♯F φ = transportf_disp_mor2 p q (♯F fg'))%mor_disp.
proof: Proof. induction p, q. refine (!_). apply transportf_disp_mor2_idpath. 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