{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {motive : CategoryTheory.LaxFunctor B C → Sort u} →
          (t : CategoryTheory.LaxFunctor B C) →
            ((toPrelaxFunctor : CategoryTheory.PrelaxFunctor B C) →
                (mapId :
                    (a : B) →
                      CategoryTheory.CategoryStruct.id (toPrelaxFunctor.obj a) ⟶
                        toPrelaxFunctor.map (CategoryTheory.CategoryStruct.id a)) →
                  (mapComp :
                      {a b c : B} →
                        (f : a ⟶ b) →
                          (g : b ⟶ c) →
                            CategoryTheory.CategoryStruct.comp (toPrelaxFunctor.map f) (toPrelaxFunctor.map g) ⟶
                              toPrelaxFunctor.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)
                              (toPrelaxFunctor.map₂ (CategoryTheory.Bicategory.whiskerRight η g)) =
                            CategoryTheory.CategoryStruct.comp
                              (CategoryTheory.Bicategory.whiskerRight (toPrelaxFunctor.map₂ η) (toPrelaxFunctor.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)
                                (toPrelaxFunctor.map₂ (CategoryTheory.Bicategory.whiskerLeft f η)) =
                              CategoryTheory.CategoryStruct.comp
                                (CategoryTheory.Bicategory.whiskerLeft (toPrelaxFunctor.map f) (toPrelaxFunctor.map₂ η))
                                (mapComp f g')) →
                        (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) (toPrelaxFunctor.map h))
                                  (CategoryTheory.CategoryStruct.comp
                                    (mapComp (CategoryTheory.CategoryStruct.comp f g) h)
                                    (toPrelaxFunctor.map₂ (CategoryTheory.Bicategory.associator f g h).hom)) =
                                CategoryTheory.CategoryStruct.comp
                                  (CategoryTheory.Bicategory.associator (toPrelaxFunctor.map f) (toPrelaxFunctor.map g)
                                      (toPrelaxFunctor.map h)).hom
                                  (CategoryTheory.CategoryStruct.comp
                                    (CategoryTheory.Bicategory.whiskerLeft (toPrelaxFunctor.map f) (mapComp g h))
                                    (mapComp f (CategoryTheory.CategoryStruct.comp g h)))) →
                          (map₂_leftUnitor :
                              ∀ {a b : B} (f : a ⟶ b),
                                toPrelaxFunctor.map₂ (CategoryTheory.Bicategory.leftUnitor f).inv =
                                  CategoryTheory.CategoryStruct.comp
                                    (CategoryTheory.Bicategory.leftUnitor (toPrelaxFunctor.map f)).inv
                                    (CategoryTheory.CategoryStruct.comp
                                      (CategoryTheory.Bicategory.whiskerRight (mapId a) (toPrelaxFunctor.map f))
                                      (mapComp (CategoryTheory.CategoryStruct.id a) f))) →
                            (map₂_rightUnitor :
                                ∀ {a b : B} (f : a ⟶ b),
                                  toPrelaxFunctor.map₂ (CategoryTheory.Bicategory.rightUnitor f).inv =
                                    CategoryTheory.CategoryStruct.comp
                                      (CategoryTheory.Bicategory.rightUnitor (toPrelaxFunctor.map f)).inv
                                      (CategoryTheory.CategoryStruct.comp
                                        (CategoryTheory.Bicategory.whiskerLeft (toPrelaxFunctor.map f) (mapId b))
                                        (mapComp f (CategoryTheory.CategoryStruct.id b)))) →
                              motive
                                { toPrelaxFunctor := toPrelaxFunctor, mapId := mapId, mapComp := mapComp,
                                  mapComp_naturality_left := mapComp_naturality_left,
                                  mapComp_naturality_right := mapComp_naturality_right,
                                  map₂_associator := map₂_associator, map₂_leftUnitor := map₂_leftUnitor,
                                  map₂_rightUnitor := map₂_rightUnitor }) →
              motive t