ruc-ai4math/mathlib_handler_benchmark_410 huggingface dataset:
-- CategoryTheory.Pseudofunctor.map₂_associator
structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u₂)
    [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
  mapId (a : B) : map (𝟙 a) ≅ 𝟙 (obj a)
  mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : map (f ≫ g) ≅ map f ≫ map g
  map₂_whisker_left :
    ∀ {a b c : B} (f : a ⟶ b) {g h : b ⟶ c} (η : g ⟶ h),
      map₂ (f ◁ η) = (mapComp f g).hom ≫ map f ◁ map₂ η ≫ (mapComp f h).inv := by
    aesop_cat
  map₂_whisker_right :
    ∀ {a b c : B} {f g : a ⟶ b} (η : f ⟶ g) (h : b ⟶ c),
      map₂ (η ▷ h) = (mapComp f h).hom ≫ map₂ η ▷ map h ≫ (mapComp g h).inv := by
    aesop_cat
  map₂_associator :
    ∀ {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
      map₂ (α_ f g h).hom = (mapComp (f ≫ g) h).hom ≫ (mapComp f g).hom ▷ map h ≫
      (α_ (map f) (map g) (map h)).hom ≫ map f ◁ (mapComp g h).inv ≫
      (mapComp f (g ≫ h)).inv := by
    aesop_cat
  map₂_left_unitor :
    ∀ {a b : B} (f : a ⟶ b),
      map₂ (λ_ f).hom = (mapComp (𝟙 a) f).hom ≫ (mapId a).hom ▷ map f ≫ (λ_ (map f)).hom := by
    aesop_cat
  map₂_right_unitor :
    ∀ {a b : B} (f : a ⟶ b),
      map₂ (ρ_ f).hom = (mapComp f (𝟙 b)).hom ≫ map f ◁ (mapId b).hom ≫ (ρ_ (map f)).hom := by
    aesop_cat
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (self : CategoryTheory.Pseudofunctor B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d)
Goal: self.map₂ (CategoryTheory.Bicategory.associator f g h).hom =
  CategoryTheory.CategoryStruct.comp (self.mapComp (CategoryTheory.CategoryStruct.comp f g) h).hom
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (self.mapComp f g).hom (self.map h))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Bicategory.associator (self.map f) (self.map g) (self.map h)).hom
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (self.map f) (self.mapComp g h).inv)
          (self.mapComp f (CategoryTheory.CategoryStruct.comp g h)).inv)))
-- CategoryTheory.Pseudofunctor.toOplax_toPrelaxFunctor
@[simps]
def toOplax : OplaxFunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C)
Goal: F.toOplax.toPrelaxFunctor = F.toPrelaxFunctor
-- CategoryTheory.Pseudofunctor.toOplax_mapComp
@[simps]
def toOplax : OplaxFunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C)
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), F.toOplax.mapComp f g = (F.mapComp f g).hom
-- CategoryTheory.Pseudofunctor.toOplax_mapId
@[simps]
def toOplax : OplaxFunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) (a : B)
Goal: F.toOplax.mapId a = (F.mapId a).hom
-- CategoryTheory.Pseudofunctor.toLax_toPrelaxFunctor
@[simps]
def toLax : LaxFunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C)
Goal: F.toLax.toPrelaxFunctor = F.toPrelaxFunctor
-- CategoryTheory.Pseudofunctor.toLax_mapComp
@[simps]
def toLax : LaxFunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C)
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), F.toLax.mapComp f g = (F.mapComp f g).inv
-- CategoryTheory.Pseudofunctor.toLax_mapId
@[simps]
def toLax : LaxFunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) (a : B)
Goal: F.toLax.mapId a = (F.mapId a).inv
-- CategoryTheory.Pseudofunctor.id_mapComp
@[simps]
def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : Pseudofunctor B B 
Arguments: (B : Type u₁) [CategoryTheory.Bicategory B]
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c),
  (CategoryTheory.Pseudofunctor.id B).mapComp f g = CategoryTheory.Iso.refl (CategoryTheory.CategoryStruct.comp f g)
-- CategoryTheory.Pseudofunctor.id_toPrelaxFunctor
@[simps]
def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : Pseudofunctor B B 
Arguments: (B : Type u₁) [CategoryTheory.Bicategory B]
Goal: (CategoryTheory.Pseudofunctor.id B).toPrelaxFunctor = CategoryTheory.PrelaxFunctor.id B
-- CategoryTheory.Pseudofunctor.id_mapId
@[simps]
def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : Pseudofunctor B B 
Arguments: (B : Type u₁) [CategoryTheory.Bicategory B] (a : B)
Goal: (CategoryTheory.Pseudofunctor.id B).mapId a = CategoryTheory.Iso.refl (CategoryTheory.CategoryStruct.id a)
-- CategoryTheory.Pseudofunctor.comp_mapId
@[simps]
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] {D : Type u₃} [CategoryTheory.Bicategory D] (F : CategoryTheory.Pseudofunctor B C) (G : CategoryTheory.Pseudofunctor C D) (a : B)
Goal: (F.comp G).mapId a = G.map₂Iso (F.mapId a) ≪≫ G.mapId (F.obj a)
-- CategoryTheory.Pseudofunctor.comp_mapComp
@[simps]
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] {D : Type u₃} [CategoryTheory.Bicategory D] (F : CategoryTheory.Pseudofunctor B C) (G : CategoryTheory.Pseudofunctor C D)
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c),
  (F.comp G).mapComp f g = G.map₂Iso (F.mapComp f g) ≪≫ G.mapComp (F.map f) (F.map g)
-- CategoryTheory.Pseudofunctor.comp_toPrelaxFunctor
@[simps]
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] {D : Type u₃} [CategoryTheory.Bicategory D] (F : CategoryTheory.Pseudofunctor B C) (G : CategoryTheory.Pseudofunctor C D)
Goal: (F.comp G).toPrelaxFunctor = F.comp G.toPrelaxFunctor
-- CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom
@[reassoc]
lemma mapComp_assoc_right_hom {c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) :
    (F.mapComp f (g ≫ h)).hom ≫ F.map f ◁ (F.mapComp g h).hom = F.map₂ (α_ f g h).inv ≫
    (F.mapComp (f ≫ g) h).hom ≫ (F.mapComp f g).hom ▷ F.map h ≫
    (α_ (F.map f) (F.map g) (F.map h)).hom 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d)
Goal: CategoryTheory.CategoryStruct.comp (F.mapComp f (CategoryTheory.CategoryStruct.comp g h)).hom
    (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapComp g h).hom) =
  CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.associator f g h).inv)
    (CategoryTheory.CategoryStruct.comp (F.mapComp (CategoryTheory.CategoryStruct.comp f g) h).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapComp f g).hom (F.map h))
        (CategoryTheory.Bicategory.associator (F.map f) (F.map g) (F.map h)).hom))
-- CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom
@[reassoc]
lemma mapComp_assoc_left_hom {c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) :
    (F.mapComp (f ≫ g) h).hom ≫ (F.mapComp f g).hom ▷ F.map h =
    F.map₂ (α_ f g h).hom ≫ (F.mapComp f (g ≫ h)).hom ≫ F.map f ◁ (F.mapComp g h).hom
    ≫ (α_ (F.map f) (F.map g) (F.map h)).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d)
Goal: CategoryTheory.CategoryStruct.comp (F.mapComp (CategoryTheory.CategoryStruct.comp f g) h).hom
    (CategoryTheory.Bicategory.whiskerRight (F.mapComp f g).hom (F.map h)) =
  CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.associator f g h).hom)
    (CategoryTheory.CategoryStruct.comp (F.mapComp f (CategoryTheory.CategoryStruct.comp g h)).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapComp g h).hom)
        (CategoryTheory.Bicategory.associator (F.map f) (F.map g) (F.map h)).inv))
-- CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv
@[reassoc]
lemma mapComp_assoc_right_inv {c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) :
    F.map f ◁ (F.mapComp g h).inv ≫ (F.mapComp f (g ≫ h)).inv =
    (α_ (F.map f) (F.map g) (F.map h)).inv ≫ (F.mapComp f g).inv ▷ F.map h ≫
    (F.mapComp (f ≫ g) h).inv ≫ F.map₂ (α_ f g h).hom 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d)
Goal: CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapComp g h).inv)
    (F.mapComp f (CategoryTheory.CategoryStruct.comp g h)).inv =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (F.map f) (F.map g) (F.map h)).inv
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapComp f g).inv (F.map h))
      (CategoryTheory.CategoryStruct.comp (F.mapComp (CategoryTheory.CategoryStruct.comp f g) h).inv
        (F.map₂ (CategoryTheory.Bicategory.associator f g h).hom)))
-- CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv
@[reassoc]
lemma mapComp_assoc_left_inv {c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) :
    (F.mapComp f g).inv ▷ F.map h ≫ (F.mapComp (f ≫ g) h).inv =
    (α_ (F.map f) (F.map g) (F.map h)).hom ≫ F.map f ◁ (F.mapComp g h).inv ≫
    (F.mapComp f (g ≫ h)).inv ≫ F.map₂ (α_ f g h).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d)
Goal: CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapComp f g).inv (F.map h))
    (F.mapComp (CategoryTheory.CategoryStruct.comp f g) h).inv =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (F.map f) (F.map g) (F.map h)).hom
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapComp g h).inv)
      (CategoryTheory.CategoryStruct.comp (F.mapComp f (CategoryTheory.CategoryStruct.comp g h)).inv
        (F.map₂ (CategoryTheory.Bicategory.associator f g h).inv)))
-- CategoryTheory.Pseudofunctor.mapComp_id_left_hom
@[reassoc]
lemma mapComp_id_left_hom (f : a ⟶ b) : (F.mapComp (𝟙 a) f).hom =
    F.map₂ (λ_ f).hom ≫ (λ_ (F.map f)).inv ≫ (F.mapId a).inv ▷ F.map f 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: (F.mapComp (CategoryTheory.CategoryStruct.id a) f).hom =
  CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.leftUnitor f).hom)
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor (F.map f)).inv
      (CategoryTheory.Bicategory.whiskerRight (F.mapId a).inv (F.map f)))
-- CategoryTheory.Pseudofunctor.mapComp_id_left
lemma mapComp_id_left (f : a ⟶ b) : (F.mapComp (𝟙 a) f) = F.map₂Iso (λ_ f) ≪≫
    (λ_ (F.map f)).symm ≪≫ (whiskerRightIso (F.mapId a) (F.map f)).symm 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: F.mapComp (CategoryTheory.CategoryStruct.id a) f =
  F.map₂Iso (CategoryTheory.Bicategory.leftUnitor f) ≪≫
    (CategoryTheory.Bicategory.leftUnitor (F.map f)).symm ≪≫
      (CategoryTheory.Bicategory.whiskerRightIso (F.mapId a) (F.map f)).symm
-- CategoryTheory.Pseudofunctor.mapComp_id_left_inv
@[reassoc]
lemma mapComp_id_left_inv (f : a ⟶ b) : (F.mapComp (𝟙 a) f).inv =
    (F.mapId a).hom ▷ F.map f ≫ (λ_ (F.map f)).hom ≫ F.map₂ (λ_ f).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: (F.mapComp (CategoryTheory.CategoryStruct.id a) f).inv =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapId a).hom (F.map f))
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor (F.map f)).hom
      (F.map₂ (CategoryTheory.Bicategory.leftUnitor f).inv))
-- CategoryTheory.Pseudofunctor.whiskerRightIso_mapId
lemma whiskerRightIso_mapId (f : a ⟶ b) : whiskerRightIso (F.mapId a) (F.map f) =
    (F.mapComp (𝟙 a) f).symm ≪≫ F.map₂Iso (λ_ f) ≪≫ (λ_ (F.map f)).symm 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: CategoryTheory.Bicategory.whiskerRightIso (F.mapId a) (F.map f) =
  (F.mapComp (CategoryTheory.CategoryStruct.id a) f).symm ≪≫
    F.map₂Iso (CategoryTheory.Bicategory.leftUnitor f) ≪≫ (CategoryTheory.Bicategory.leftUnitor (F.map f)).symm
-- CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom
@[reassoc]
lemma whiskerRight_mapId_hom (f : a ⟶ b) : (F.mapId a).hom ▷ F.map f =
    (F.mapComp (𝟙 a) f).inv ≫ F.map₂ (λ_ f).hom ≫ (λ_ (F.map f)).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: CategoryTheory.Bicategory.whiskerRight (F.mapId a).hom (F.map f) =
  CategoryTheory.CategoryStruct.comp (F.mapComp (CategoryTheory.CategoryStruct.id a) f).inv
    (CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.leftUnitor f).hom)
      (CategoryTheory.Bicategory.leftUnitor (F.map f)).inv)
-- CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv
@[reassoc]
lemma whiskerRight_mapId_inv (f : a ⟶ b) : (F.mapId a).inv ▷ F.map f =
    (λ_ (F.map f)).hom ≫ F.map₂ (λ_ f).inv ≫ (F.mapComp (𝟙 a) f).hom 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: CategoryTheory.Bicategory.whiskerRight (F.mapId a).inv (F.map f) =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor (F.map f)).hom
    (CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.leftUnitor f).inv)
      (F.mapComp (CategoryTheory.CategoryStruct.id a) f).hom)
-- CategoryTheory.Pseudofunctor.mapComp_id_right_hom
@[reassoc]
lemma mapComp_id_right_hom (f : a ⟶ b) : (F.mapComp f (𝟙 b)).hom =
    F.map₂ (ρ_ f).hom ≫ (ρ_ (F.map f)).inv ≫ F.map f ◁ (F.mapId b).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: (F.mapComp f (CategoryTheory.CategoryStruct.id b)).hom =
  CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.rightUnitor f).hom)
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor (F.map f)).inv
      (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapId b).inv))
-- CategoryTheory.Pseudofunctor.mapComp_id_right
lemma mapComp_id_right (f : a ⟶ b) : (F.mapComp f (𝟙 b)) = F.map₂Iso (ρ_ f) ≪≫
    (ρ_ (F.map f)).symm ≪≫ (whiskerLeftIso (F.map f) (F.mapId b)).symm 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: F.mapComp f (CategoryTheory.CategoryStruct.id b) =
  F.map₂Iso (CategoryTheory.Bicategory.rightUnitor f) ≪≫
    (CategoryTheory.Bicategory.rightUnitor (F.map f)).symm ≪≫
      (CategoryTheory.Bicategory.whiskerLeftIso (F.map f) (F.mapId b)).symm
-- CategoryTheory.Pseudofunctor.mapComp_id_right_inv
@[reassoc]
lemma mapComp_id_right_inv (f : a ⟶ b) : (F.mapComp f (𝟙 b)).inv =
    F.map f ◁ (F.mapId b).hom ≫ (ρ_ (F.map f)).hom ≫ F.map₂ (ρ_ f).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: (F.mapComp f (CategoryTheory.CategoryStruct.id b)).inv =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapId b).hom)
    (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor (F.map f)).hom
      (F.map₂ (CategoryTheory.Bicategory.rightUnitor f).inv))
-- CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId
lemma whiskerLeftIso_mapId (f : a ⟶ b) : whiskerLeftIso (F.map f) (F.mapId b) =
    (F.mapComp f (𝟙 b)).symm ≪≫ F.map₂Iso (ρ_ f) ≪≫ (ρ_ (F.map f)).symm 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: CategoryTheory.Bicategory.whiskerLeftIso (F.map f) (F.mapId b) =
  (F.mapComp f (CategoryTheory.CategoryStruct.id b)).symm ≪≫
    F.map₂Iso (CategoryTheory.Bicategory.rightUnitor f) ≪≫ (CategoryTheory.Bicategory.rightUnitor (F.map f)).symm
-- CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom
@[reassoc]
lemma whiskerLeft_mapId_hom (f : a ⟶ b) : F.map f ◁ (F.mapId b).hom =
    (F.mapComp f (𝟙 b)).inv ≫ F.map₂ (ρ_ f).hom ≫ (ρ_ (F.map f)).inv 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapId b).hom =
  CategoryTheory.CategoryStruct.comp (F.mapComp f (CategoryTheory.CategoryStruct.id b)).inv
    (CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.rightUnitor f).hom)
      (CategoryTheory.Bicategory.rightUnitor (F.map f)).inv)
-- CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv
@[reassoc]
lemma whiskerLeft_mapId_inv (f : a ⟶ b) : F.map f ◁ (F.mapId b).inv =
    (ρ_ (F.map f)).hom ≫ F.map₂ (ρ_ f).inv ≫ (F.mapComp f (𝟙 b)).hom 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {a b : B} (f : a ⟶ b)
Goal: CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapId b).inv =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor (F.map f)).hom
    (CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.rightUnitor f).inv)
      (F.mapComp f (CategoryTheory.CategoryStruct.id b)).hom)
-- CategoryTheory.Pseudofunctor.mkOfOplax_toPrelaxFunctor
@[simps]
def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) (F' : F.PseudoCore)
Goal: (CategoryTheory.Pseudofunctor.mkOfOplax F F').toPrelaxFunctor = F.toPrelaxFunctor
-- CategoryTheory.Pseudofunctor.mkOfOplax_mapComp
@[simps]
def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) (F' : F.PseudoCore)
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), (CategoryTheory.Pseudofunctor.mkOfOplax F F').mapComp f g = F'.mapCompIso f g
-- CategoryTheory.Pseudofunctor.mkOfOplax_mapId
@[simps]
def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) (F' : F.PseudoCore) (a : B)
Goal: (CategoryTheory.Pseudofunctor.mkOfOplax F F').mapId a = F'.mapIdIso a
-- CategoryTheory.Pseudofunctor.mkOfOplax'_mapComp_hom
@[simps!]
noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.mapId a)]
    [∀ {a b c} (f : a ⟶ b) (g : b ⟶ c), IsIso (F.mapComp f g)] : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) [∀ (a : B), CategoryTheory.IsIso (F.mapId a)] [∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), CategoryTheory.IsIso (F.mapComp f g)]
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), ((CategoryTheory.Pseudofunctor.mkOfOplax' F).mapComp f g).hom = F.mapComp f g
-- CategoryTheory.Pseudofunctor.mkOfOplax'_mapComp_inv
@[simps!]
noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.mapId a)]
    [∀ {a b c} (f : a ⟶ b) (g : b ⟶ c), IsIso (F.mapComp f g)] : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) [∀ (a : B), CategoryTheory.IsIso (F.mapId a)] [∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), CategoryTheory.IsIso (F.mapComp f g)]
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c),
  ((CategoryTheory.Pseudofunctor.mkOfOplax' F).mapComp f g).inv = CategoryTheory.inv (F.mapComp f g)
-- CategoryTheory.Pseudofunctor.mkOfOplax'_mapId_hom
@[simps!]
noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.mapId a)]
    [∀ {a b c} (f : a ⟶ b) (g : b ⟶ c), IsIso (F.mapComp f g)] : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) [∀ (a : B), CategoryTheory.IsIso (F.mapId a)] [∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), CategoryTheory.IsIso (F.mapComp f g)] (a : B)
Goal: ((CategoryTheory.Pseudofunctor.mkOfOplax' F).mapId a).hom = F.mapId a
-- CategoryTheory.Pseudofunctor.mkOfOplax'_toPrelaxFunctor
@[simps!]
noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.mapId a)]
    [∀ {a b c} (f : a ⟶ b) (g : b ⟶ c), IsIso (F.mapComp f g)] : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) [∀ (a : B), CategoryTheory.IsIso (F.mapId a)] [∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), CategoryTheory.IsIso (F.mapComp f g)]
Goal: (CategoryTheory.Pseudofunctor.mkOfOplax' F).toPrelaxFunctor = F.toPrelaxFunctor
-- CategoryTheory.Pseudofunctor.mkOfOplax'_mapId_inv
@[simps!]
noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.mapId a)]
    [∀ {a b c} (f : a ⟶ b) (g : b ⟶ c), IsIso (F.mapComp f g)] : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.OplaxFunctor B C) [∀ (a : B), CategoryTheory.IsIso (F.mapId a)] [∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), CategoryTheory.IsIso (F.mapComp f g)] (a : B)
Goal: ((CategoryTheory.Pseudofunctor.mkOfOplax' F).mapId a).inv = CategoryTheory.inv (F.mapId a)
-- CategoryTheory.Pseudofunctor.mkOfLax_mapId
@[simps]
def mkOfLax (F : LaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.LaxFunctor B C) (F' : F.PseudoCore) (a : B)
Goal: (CategoryTheory.Pseudofunctor.mkOfLax F F').mapId a = F'.mapIdIso a
-- CategoryTheory.Pseudofunctor.mkOfLax_mapComp
@[simps]
def mkOfLax (F : LaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.LaxFunctor B C) (F' : F.PseudoCore)
Goal: ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), (CategoryTheory.Pseudofunctor.mkOfLax F F').mapComp f g = F'.mapCompIso f g
-- CategoryTheory.Pseudofunctor.mkOfLax_toPrelaxFunctor
@[simps]
def mkOfLax (F : LaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.LaxFunctor B C) (F' : F.PseudoCore)
Goal: (CategoryTheory.Pseudofunctor.mkOfLax F F').toPrelaxFunctor = F.toPrelaxFunctor
-- CategoryTheory.Pseudofunctor.mkOfLax'_mapId_inv
@[simps!]
noncomputable def mkOfLax' (F : LaxFunctor B C) [∀ a, IsIso (F.mapId a)]
    [∀ {a b c} (f : a ⟶ b) (g : b ⟶ c), IsIso (F.mapComp f g)] : Pseudofunctor B C 
Arguments: {B : Type u₁} [CategoryTheory.Bicategory B] {C : Type u₂} [CategoryTheory.Bicategory C] (F : CategoryTheory.LaxFunctor B C) [∀ (a : B), CategoryTheory.IsIso (F.mapId a)] [∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), CategoryTheory.IsIso (F.mapComp f g)] (a : B)
Goal: ((CategoryTheory.Pseudofunctor.mkOfLax' F).mapId a).inv = F.mapId a