{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {motive : CategoryTheory.StrictlyUnitaryLaxFunctorCore B C → Sort u} →
          ((obj : B → C) →
              (map : {X Y : B} → (X ⟶ Y) → (obj X ⟶ obj Y)) →
                (map_id :
                    ∀ (X : B), map (CategoryTheory.CategoryStruct.id X) = CategoryTheory.CategoryStruct.id (obj X)) →
                  (map₂ : {a b : B} → {f g : a ⟶ b} → (f ⟶ g) → (map f ⟶ map g)) →
                    (map₂_id :
                        ∀ {a b : B} (f : a ⟶ b),
                          map₂ (CategoryTheory.CategoryStruct.id f) = CategoryTheory.CategoryStruct.id (map f)) →
                      (map₂_comp :
                          ∀ {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h),
                            map₂ (CategoryTheory.CategoryStruct.comp η θ) =
                              CategoryTheory.CategoryStruct.comp (map₂ η) (map₂ θ)) →
                        (mapComp :
                            {a b c : B} →
                              (f : a ⟶ b) →
                                (g : b ⟶ c) →
                                  CategoryTheory.CategoryStruct.comp (map f) (map g) ⟶
                                    map (CategoryTheory.CategoryStruct.comp f g)) →
                          (mapComp_naturality_left :
                              ∀ {a b c : B} {f f' : a ⟶ b} (η : f ⟶ f') (g : b ⟶ c),
                                CategoryTheory.CategoryStruct.comp (mapComp f g)
                                    (map₂ (CategoryTheory.Bicategory.whiskerRight η g)) =
                                  CategoryTheory.CategoryStruct.comp
                                    (CategoryTheory.Bicategory.whiskerRight (map₂ η) (map g)) (mapComp f' g)) →
                            (mapComp_naturality_right :
                                ∀ {a b c : B} (f : a ⟶ b) {g g' : b ⟶ c} (η : g ⟶ g'),
                                  CategoryTheory.CategoryStruct.comp (mapComp f g)
                                      (map₂ (CategoryTheory.Bicategory.whiskerLeft f η)) =
                                    CategoryTheory.CategoryStruct.comp
                                      (CategoryTheory.Bicategory.whiskerLeft (map f) (map₂ η)) (mapComp f g')) →
                              (map₂_leftUnitor :
                                  ∀ {a b : B} (f : a ⟶ b),
                                    map₂ (CategoryTheory.Bicategory.leftUnitor f).inv =
                                      CategoryTheory.CategoryStruct.comp
                                        (CategoryTheory.Bicategory.leftUnitor (map f)).inv
                                        (CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯)
                                          (mapComp (CategoryTheory.CategoryStruct.id a) f))) →
                                (map₂_rightUnitor :
                                    ∀ {a b : B} (f : a ⟶ b),
                                      map₂ (CategoryTheory.Bicategory.rightUnitor f).inv =
                                        CategoryTheory.CategoryStruct.comp
                                          (CategoryTheory.Bicategory.rightUnitor (map f)).inv
                                          (CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯)
                                            (mapComp f (CategoryTheory.CategoryStruct.id b)))) →
                                  (map₂_associator :
                                      ∀ {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
                                        CategoryTheory.CategoryStruct.comp
                                            (CategoryTheory.Bicategory.whiskerRight (mapComp f g) (map h))
                                            (CategoryTheory.CategoryStruct.comp
                                              (mapComp (CategoryTheory.CategoryStruct.comp f g) h)
                                              (map₂ (CategoryTheory.Bicategory.associator f g h).hom)) =
                                          CategoryTheory.CategoryStruct.comp
                                            (CategoryTheory.Bicategory.associator (map f) (map g) (map h)).hom
                                            (CategoryTheory.CategoryStruct.comp
                                              (CategoryTheory.Bicategory.whiskerLeft (map f) (mapComp g h))
                                              (mapComp f (CategoryTheory.CategoryStruct.comp g h)))) →
                                    motive
                                      { obj := obj, map := map, map_id := map_id, map₂ := map₂, map₂_id := map₂_id,
                                        map₂_comp := map₂_comp, mapComp := mapComp,
                                        mapComp_naturality_left := mapComp_naturality_left,
                                        mapComp_naturality_right := mapComp_naturality_right,
                                        map₂_leftUnitor := map₂_leftUnitor, map₂_rightUnitor := map₂_rightUnitor,
                                        map₂_associator := map₂_associator }) →
            (t : CategoryTheory.StrictlyUnitaryLaxFunctorCore B C) → motive t