awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : C ⥤ Functor.{v_2, v_2, u_2, u_2} D D
X : C
e : F.obj X ≅ 𝟭 D
inst_5 : ∀ (Y : D), PreservesColimit (Functor.empty C) (F.flip.obj Y)
p : I × J → J
hp : ∀ (j : J), p (0, j) = j
Y Y' : GradedObject J D
φ : Y ⟶ Y'
inst_6 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y).HasMap p
inst_7 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y').HasMap p
⊢ Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')))
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ)
have rw : Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
  (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')) ≫
    Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
  ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
Tactic: rw [← cancel_mono (mapBifunctorLeftUnitor F X e p hp Y').inv, assoc, assoc, Iso.hom_inv_id,
    comp_id, mapBifunctorLeftUnitor_inv_naturality, Iso.hom_inv_id_assoc]
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : C ⥤ Functor.{v_2, v_2, u_2, u_2} D D
X : C
e : F.obj X ≅ 𝟭 D
inst_5 : ∀ (Y : D), PreservesColimit (Functor.empty C) (F.flip.obj Y)
p : I × J → J
hp : ∀ (j : J), p (0, j) = j
Y Y' : GradedObject J D
φ : Y ⟶ Y'
inst_6 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y).HasMap p
inst_7 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y').HasMap p
rw :
  Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
        (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')) ≫
      Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
    ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
⊢ Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')))
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ)
have rw₁ : Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
  (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ)
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y') ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y')))
  ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
Tactic: rw [← cancel_mono (mapBifunctorLeftUnitor F X e p hp Y').inv, assoc, assoc, Iso.hom_inv_id,
    comp_id, mapBifunctorLeftUnitor_inv_naturality, Iso.hom_inv_id_assoc]
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : C ⥤ Functor.{v_2, v_2, u_2, u_2} D D
X : C
e : F.obj X ≅ 𝟭 D
inst_5 : ∀ (Y : D), PreservesColimit (Functor.empty C) (F.flip.obj Y)
p : I × J → J
hp : ∀ (j : J), p (0, j) = j
Y Y' : GradedObject J D
φ : Y ⟶ Y'
inst_6 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y).HasMap p
inst_7 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y').HasMap p
rw :
  Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
        (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')) ≫
      Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
    ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
rw₁ :
  Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ)
      (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y') ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y')))
    ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
⊢ Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')))
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ)
have rw₂ : Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
  (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ)
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y') ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y')))
  (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
Tactic: rw [← cancel_mono (mapBifunctorLeftUnitor F X e p hp Y').inv, assoc, assoc, Iso.hom_inv_id,
    comp_id, mapBifunctorLeftUnitor_inv_naturality, Iso.hom_inv_id_assoc]
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : C ⥤ Functor.{v_2, v_2, u_2, u_2} D D
X : C
e : F.obj X ≅ 𝟭 D
inst_5 : ∀ (Y : D), PreservesColimit (Functor.empty C) (F.flip.obj Y)
p : I × J → J
hp : ∀ (j : J), p (0, j) = j
Y Y' : GradedObject J D
φ : Y ⟶ Y'
inst_6 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y).HasMap p
inst_7 : (((mapBifunctor F I J).obj (Functor.obj (single₀ I) X)).obj Y').HasMap p
rw :
  Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
        (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')) ≫
      Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
    ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
rw₁ :
  Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ)
      (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y') ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y')))
    ((Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ) ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
rw₂ :
  Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ)
      (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y') ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y')))
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
⊢ Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ Y')
    (CategoryStruct.comp (Y := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
      (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ) (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y')))
    (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ)
have rw₃ : Eq (α := mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y ⟶ mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y')
  (mapBifunctorMapMap F p (𝟙 (Functor.obj (single₀ I) X)) φ ≫ 𝟙 (mapBifunctorMapObj F p (Functor.obj (single₀ I) X) Y'))
  (Iso.hom (mapBifunctorLeftUnitor F X e p hp Y) ≫ φ ≫ Iso.inv (mapBifunctorLeftUnitor F X e p hp Y'))
Tactic: rw [← cancel_mono (mapBifunctorLeftUnitor F X e p hp Y').inv, assoc, assoc, Iso.hom_inv_id,
    comp_id, mapBifunctorLeftUnitor_inv_naturality, Iso.hom_inv_id_assoc]
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : D ⥤ Functor.{v_1, v_2, u_1, u_2} C D
Y : C
e : F.flip.obj Y ≅ 𝟭 D
inst_5 : ∀ (X : D), PreservesColimit (Functor.empty C) (F.obj X)
p : J × I → J
hp : ∀ (j : J), p (j, 0) = j
X X' : GradedObject J D
φ : X ⟶ X'
j : J
s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)
j' : J
i : I
h : (j', i) ∈ p ⁻¹' {j}
⊢ Eq (α :=
    (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h) ⟶
      s.pt)
    (CategoryStruct.comp (Y :=
      Cocone.pt (F := Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
        (mapBifunctorRightUnitorCofan F Y e p hp X j))
      (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j)
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h))
      ((fun (s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)) ↦
          (e.inv.app (X j) ≫
              CategoryStruct.comp (Y := (F.obj (X j)).obj (Functor.obj (single 0) Y 0))
                ((F.obj (X j)).map (Iso.inv (singleObjApplyIso 0 Y)))
                (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j, 0) ⋯)) :
            Cocone.pt (F :=
                Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
                (mapBifunctorRightUnitorCofan F Y e p hp X j) ⟶
              s.pt))
        s))
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h))
have pos : ∀ (hi : i = 0),
  Eq (α :=
    (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h) ⟶
      s.pt)
    (CategoryStruct.comp (Y :=
      Cocone.pt (F := Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
        (mapBifunctorRightUnitorCofan F Y e p hp X j))
      (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j)
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h))
      ((fun (s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)) ↦
          (e.inv.app (X j) ≫
              CategoryStruct.comp (Y := (F.obj (X j)).obj (Functor.obj (single 0) Y 0))
                ((F.obj (X j)).map (Iso.inv (singleObjApplyIso 0 Y)))
                (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j, 0) sorry)) :
            Cocone.pt (F :=
                Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
                (mapBifunctorRightUnitorCofan F Y e p hp X j) ⟶
              s.pt))
        s))
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h))
Tactic: by_cases hi : i = 0
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : D ⥤ Functor.{v_1, v_2, u_1, u_2} C D
Y : C
e : F.flip.obj Y ≅ 𝟭 D
inst_5 : ∀ (X : D), PreservesColimit (Functor.empty C) (F.obj X)
p : J × I → J
hp : ∀ (j : J), p (j, 0) = j
X X' : GradedObject J D
φ : X ⟶ X'
j : J
s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)
j' : J
i : I
h : (j', i) ∈ p ⁻¹' {j}
hi : i = 0
⊢ Eq (α :=
    (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h) ⟶
      s.pt)
    (CategoryStruct.comp (Y :=
      Cocone.pt (F := Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
        (mapBifunctorRightUnitorCofan F Y e p hp X j))
      (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j)
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h))
      ((fun (s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)) ↦
          (e.inv.app (X j) ≫
              CategoryStruct.comp (Y := (F.obj (X j)).obj (Functor.obj (single 0) Y 0))
                ((F.obj (X j)).map (Iso.inv (singleObjApplyIso 0 Y)))
                (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j, 0) ⋯)) :
            Cocone.pt (F :=
                Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
                (mapBifunctorRightUnitorCofan F Y e p hp X j) ⟶
              s.pt))
        s))
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', i) h))
have pos : ∀ (h : (j', 0) ∈ p ⁻¹' {j}),
  Eq (α :=
    (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', 0) h) ⟶
      s.pt)
    (CategoryStruct.comp (Y :=
      Cocone.pt (F := Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
        (mapBifunctorRightUnitorCofan F Y e p hp X j))
      (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j)
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', 0) h))
      ((fun (s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)) ↦
          (e.inv.app (X j) ≫
              CategoryStruct.comp (Y := (F.obj (X j)).obj (Functor.obj (single 0) Y 0))
                ((F.obj (X j)).map (Iso.inv (singleObjApplyIso 0 Y)))
                (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j, 0) sorry)) :
            Cocone.pt (F :=
                Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
                (mapBifunctorRightUnitorCofan F Y e p hp X j) ⟶
              s.pt))
        s))
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', 0) h))
Tactic: subst hi
Cleared hypotheses: i, h, hi
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (hypothesis)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : D ⥤ Functor.{v_1, v_2, u_1, u_2} C D
Y : C
e : F.flip.obj Y ≅ 𝟭 D
inst_5 : ∀ (X : D), PreservesColimit (Functor.empty C) (F.obj X)
p : J × I → J
hp : ∀ (j : J), p (j, 0) = j
X X' : GradedObject J D
φ : X ⟶ X'
j : J
s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)
j' : J
h : (j', 0) ∈ p ⁻¹' {j}
⊢ Eq (α :=
    (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', 0) h) ⟶
      s.pt)
    (CategoryStruct.comp (Y :=
      Cocone.pt (F := Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
        (mapBifunctorRightUnitorCofan F Y e p hp X j))
      (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j)
        (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', 0) h))
      ((fun (s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j)) ↦
          (e.inv.app (X j) ≫
              CategoryStruct.comp (Y := (F.obj (X j)).obj (Functor.obj (single 0) Y 0))
                ((F.obj (X j)).map (Iso.inv (singleObjApplyIso 0 Y)))
                (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j, 0) ⋯)) :
            Cocone.pt (F :=
                Discrete.functor ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j))
                (mapBifunctorRightUnitorCofan F Y e p hp X j) ⟶
              s.pt))
        s))
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j}) (j', 0) h))
have h₁ : j' = j
Tactic: simp only [Set.mem_preimage, hp, Set.mem_singleton_iff] at h
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : D ⥤ Functor.{v_1, v_2, u_1, u_2} C D
Y : C
e : F.flip.obj Y ≅ 𝟭 D
inst_5 : ∀ (X : D), PreservesColimit (Functor.empty C) (F.obj X)
p : J × I → J
hp : ∀ (j : J), p (j, 0) = j
X X' : GradedObject J D
φ : X ⟶ X'
j' : J
s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j')
h : (j', 0) ∈ p ⁻¹' {j'}
⊢ Eq (α := (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
    (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j')
          (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h) ≫
        e.inv.app (X j') ≫
          CategoryStruct.comp (Y := (F.obj (X j')).obj (Functor.obj (single 0) Y 0))
            ((F.obj (X j')).map (Iso.inv (singleObjApplyIso 0 Y)))
            (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) ⋯)) :
      (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h) :
      (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j'
          (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h) ⟶
        s.pt)
have pos : Eq (α := (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
  (((F.obj (X j')).map (Iso.hom (singleObjApplyIso 0 Y)) ≫ e.hom.app (X j')) ≫
    e.inv.app (X j') ≫
      CategoryStruct.comp (Y := (F.obj (X j')).obj (Functor.obj (single 0) Y 0))
        ((F.obj (X j')).map (Iso.inv (singleObjApplyIso 0 Y)))
        (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) sorry)))
  (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h))
Tactic: rw [mapBifunctorRightUnitorCofan_inj, assoc, Iso.hom_inv_id_app_assoc,
          ← Functor.map_comp_assoc, Iso.hom_inv_id, Functor.map_id, id_comp]
-- Lean 4 proof step from Mathlib.CategoryTheory.GradedObject.Unitor (goal)
Goal:
C : Type u_1
D : Type u_2
I : Type u_3
J : Type u_4
inst : Category.{v_1, u_1} C
inst_1 : Category.{v_2, u_2} D
inst_2 : Zero I
inst_3 : DecidableEq I
inst_4 : HasInitial.{v_1, u_1} C
F : D ⥤ Functor.{v_1, v_2, u_1, u_2} C D
Y : C
e : F.flip.obj Y ≅ 𝟭 D
inst_5 : ∀ (X : D), PreservesColimit (Functor.empty C) (F.obj X)
p : J × I → J
hp : ∀ (j : J), p (j, 0) = j
X X' : GradedObject J D
φ : X ⟶ X'
j' : J
s : Cofan ((((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j')
h : (j', 0) ∈ p ⁻¹' {j'}
pos :
  Eq (α := (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
    (((F.obj (X j')).map (Iso.hom (singleObjApplyIso 0 Y)) ≫ e.hom.app (X j')) ≫
      e.inv.app (X j') ≫
        CategoryStruct.comp (Y := (F.obj (X j')).obj (Functor.obj (single 0) Y 0))
          ((F.obj (X j')).map (Iso.inv (singleObjApplyIso 0 Y)))
          (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) ⋯)))
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h))
⊢ Eq (α := (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
    (Cofan.inj (mapBifunctorRightUnitorCofan F Y e p hp X j')
          (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h) ≫
        e.inv.app (X j') ≫
          CategoryStruct.comp (Y := (F.obj (X j')).obj (Functor.obj (single 0) Y 0))
            ((F.obj (X j')).map (Iso.inv (singleObjApplyIso 0 Y)))
            (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) ⋯)) :
      (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
    (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h) :
      (((mapBifunctor F J I).obj X).obj (Functor.obj (single₀ I) Y)).mapObjFun p j'
          (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h) ⟶
        s.pt)
have pos₁ : Eq (α := (F.obj (X j')).obj (Functor.obj (single₀ I) Y 0) ⟶ s.pt)
  ((F.obj (X j')).map (Iso.hom (singleObjApplyIso 0 Y)) ≫
    e.hom.app (X j') ≫
      e.inv.app (X j') ≫
        CategoryStruct.comp (Y := (F.obj (X j')).obj (Functor.obj (single 0) Y 0))
          ((F.obj (X j')).map (Iso.inv (singleObjApplyIso 0 Y)))
          (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) sorry)))
  (s.inj (Subtype.mk (p := fun (x : J × I) ↦ x ∈ p ⁻¹' {j'}) (j', 0) h))
Tactic: rw [mapBifunctorRightUnitorCofan_inj, assoc, Iso.hom_inv_id_app_assoc,
          ← Functor.map_comp_assoc, Iso.hom_inv_id, Functor.map_id, id_comp]