awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
    (Iso.inv K.rightUnitor' i : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
    (Iso.inv (ρ_ (K.X i)) ≫
        K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
          K.ιTensorObj (tensorUnit C c) i 0 i ⋯ :
      K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
have dsimp : Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
  (CategoryStruct.comp (Y :=
      GradedObject.Monoidal.tensorObj.{u_2, v_1, u_1} K.X
        (Functor.obj (GradedObject.single₀ I) (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) i)
      (Iso.inv (GradedObject.Monoidal.rightUnitor K.X) i)
      (GradedObject.Monoidal.tensorHom (𝟙 K.X) (Iso.hom (tensorUnitIso C c)) i) :
    K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
  (Iso.inv (ρ_ (K.X i)) ≫
      K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
        K.ιTensorObj (tensorUnit C c) i 0 i sorry :
    K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
Tactic: dsimp [rightUnitor']
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
    (CategoryStruct.comp (Y :=
        GradedObject.Monoidal.tensorObj.{u_2, v_1, u_1} K.X
          (Functor.obj (GradedObject.single₀ I) (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) i)
        (Iso.inv (GradedObject.Monoidal.rightUnitor K.X) i)
        (GradedObject.Monoidal.tensorHom (𝟙 K.X) (Iso.hom (tensorUnitIso C c)) i) :
      K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
    (Iso.inv (ρ_ (K.X i)) ≫
        K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
          K.ιTensorObj (tensorUnit C c) i 0 i ⋯ :
      K.X i ⟶ (K.tensorObj (tensorUnit C c)).X i)
have rw : Eq (α :=
  MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
      (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) ⟶
    (K.tensorObj (tensorUnit C c)).X i)
  (CategoryStruct.comp (Y :=
    MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
      (GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0))
    (K.X i ◁ Iso.inv GradedObject.Monoidal.tensorUnit₀)
    (CategoryStruct.comp (Y :=
      MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i) (X.{v_1, u_1, u_2} (tensorUnit C c) 0))
      (𝟙 K.X i ⊗ₘ Iso.hom (tensorUnitIso C c) 0)
      (GradedObject.Monoidal.ιTensorObj K.X (X.{v_1, u_1, u_2} (tensorUnit C c)) i 0 i sorry)))
  (K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
    K.ιTensorObj (tensorUnit C c) i 0 i sorry)
Tactic: rw [GradedObject.Monoidal.rightUnitor_inv_apply, assoc, assoc, Iso.cancel_iso_inv_left,
    GradedObject.Monoidal.ι_tensorHom]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq (α :=
    MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
        (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) ⟶
      (K.tensorObj (tensorUnit C c)).X i)
    (CategoryStruct.comp (Y :=
      MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
        (GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0))
      (K.X i ◁ Iso.inv GradedObject.Monoidal.tensorUnit₀)
      (CategoryStruct.comp (Y :=
        MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i) (X.{v_1, u_1, u_2} (tensorUnit C c) 0))
        (𝟙 K.X i ⊗ₘ Iso.hom (tensorUnitIso C c) 0)
        (GradedObject.Monoidal.ιTensorObj K.X (X.{v_1, u_1, u_2} (tensorUnit C c)) i 0 i ⋯)))
    (K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
      K.ιTensorObj (tensorUnit C c) i 0 i ⋯)
have dsimp : Eq (α :=
  MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
      (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) ⟶
    (K.tensorObj (tensorUnit C c)).X i)
  (CategoryStruct.comp (Y :=
    MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
      (GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0))
    (K.X i ◁ Iso.inv GradedObject.Monoidal.tensorUnit₀)
    (CategoryStruct.comp (Y :=
      MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i) (X.{v_1, u_1, u_2} (tensorUnit C c) 0))
      (𝟙 (K.X i) ⊗ₘ Iso.hom (tensorUnitIso C c) 0)
      (GradedObject.Monoidal.ιTensorObj K.X (X.{v_1, u_1, u_2} (tensorUnit C c)) i 0 i sorry)))
  (K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
    K.ιTensorObj (tensorUnit C c) i 0 i sorry)
Tactic: dsimp
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq (α :=
    MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
        (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) ⟶
      (K.tensorObj (tensorUnit C c)).X i)
    (CategoryStruct.comp (Y :=
      MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
        (GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0))
      (K.X i ◁ Iso.inv GradedObject.Monoidal.tensorUnit₀)
      (CategoryStruct.comp (Y :=
        MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i) (X.{v_1, u_1, u_2} (tensorUnit C c) 0))
        (𝟙 (K.X i) ⊗ₘ Iso.hom (tensorUnitIso C c) 0)
        (GradedObject.Monoidal.ιTensorObj K.X (X.{v_1, u_1, u_2} (tensorUnit C c)) i 0 i ⋯)))
    (K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
      K.ιTensorObj (tensorUnit C c) i 0 i ⋯)
have rw : Eq (α :=
  MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
      (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) ⟶
    (K.tensorObj (tensorUnit C c)).X i)
  (CategoryStruct.comp (Y :=
    MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i) (X.{v_1, u_1, u_2} (tensorUnit C c) 0))
    (K.X i ◁
      CategoryStruct.comp (Y := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0)
        (Iso.inv GradedObject.Monoidal.tensorUnit₀) (Iso.hom (tensorUnitIso C c) 0))
    (GradedObject.Monoidal.ιTensorObj K.X (X.{v_1, u_1, u_2} (tensorUnit C c)) i 0 i sorry))
  (K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
    K.ιTensorObj (tensorUnit C c) i 0 i sorry)
Tactic: rw [id_tensorHom, ← whiskerLeft_comp_assoc]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq (α :=
    MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i)
        (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) ⟶
      (K.tensorObj (tensorUnit C c)).X i)
    (CategoryStruct.comp (Y :=
      MonoidalCategoryStruct.tensorObj.{v_1, u_1} (𝒞 := inst) (K.X i) (X.{v_1, u_1, u_2} (tensorUnit C c) 0))
      (K.X i ◁
        CategoryStruct.comp (Y := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0)
          (Iso.inv GradedObject.Monoidal.tensorUnit₀) (Iso.hom (tensorUnitIso C c) 0))
      (GradedObject.Monoidal.ιTensorObj K.X (X.{v_1, u_1, u_2} (tensorUnit C c)) i 0 i ⋯))
    (K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
      K.ιTensorObj (tensorUnit C c) i 0 i ⋯)
have e_a : Eq (α := MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst) ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
  (CategoryStruct.comp (Y := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0)
    (Iso.inv GradedObject.Monoidal.tensorUnit₀) (Iso.hom (tensorUnitIso C c) 0))
  (Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))))
Tactic: congr 2
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq (α := MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst) ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
    (CategoryStruct.comp (Y := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0)
      (Iso.inv GradedObject.Monoidal.tensorUnit₀) (Iso.hom (tensorUnitIso C c) 0))
    (Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))))
have e_a : Eq.{v_1 + 1} (α := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
  (Iso.hom (tensorUnitIso C c) 0 :
    Functor.obj (GradedObject.single₀ I) (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 ⟶
      X.{v_1, u_1, u_2} (tensorUnit C c) 0)
  (Iso.hom GradedObject.Monoidal.tensorUnit₀ ≫
      Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) :
    GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
Tactic: rw [← cancel_epi (GradedObject.Monoidal.tensorUnit₀ (I := I)).hom, Iso.hom_inv_id_assoc]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq.{v_1 + 1} (α := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
    (Iso.hom (tensorUnitIso C c) 0 :
      Functor.obj (GradedObject.single₀ I) (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 ⟶
        X.{v_1, u_1, u_2} (tensorUnit C c) 0)
    (Iso.hom GradedObject.Monoidal.tensorUnit₀ ≫
        Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) :
      GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
have e_a : Eq (α := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
  (Iso.hom
    (if hi : Eq.{u_2 + 1} (α := I) 0 0 then
      GradedObject.singleObjApplyIsoOfEq 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 hi ≪≫
        Iso.symm (singleObjXIsoOfEq c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 hi)
    else { hom := 0, inv := 0, hom_inv_id := sorry, inv_hom_id := sorry }))
  (Iso.hom GradedObject.Monoidal.tensorUnit₀ ≫
    Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))))
Tactic: dsimp [tensorUnitIso]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i : I
⊢ Eq (α := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
    (Iso.hom
      (if hi : Eq.{u_2 + 1} (α := I) 0 0 then
        GradedObject.singleObjApplyIsoOfEq 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 hi ≪≫
          Iso.symm (singleObjXIsoOfEq c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 hi)
      else { hom := 0, inv := 0, hom_inv_id := ⋯, inv_hom_id := ⋯ }))
    (Iso.hom GradedObject.Monoidal.tensorUnit₀ ≫
      Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))))
have e_a : Eq (α := GradedObject.Monoidal.tensorUnit.{u_2, v_1, u_1} (I := I) 0 ⟶ X.{v_1, u_1, u_2} (tensorUnit C c) 0)
  (Iso.hom
    (GradedObject.singleObjApplyIsoOfEq 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 sorry ≪≫
      Iso.symm (singleObjXIsoOfEq c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst)) 0 sorry)))
  (Iso.hom GradedObject.Monoidal.tensorUnit₀ ≫
    Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))))
Tactic: rw [dif_pos rfl]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i j : I
⊢ Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (Iso.inv K.rightUnitor' i ≫ (K.tensorObj (tensorUnit C c)).d i j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (K.d i j ≫ Iso.inv K.rightUnitor' j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
have pos : ∀ (hij : c.Rel i j),
  Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (Iso.inv K.rightUnitor' i ≫ (K.tensorObj (tensorUnit C c)).d i j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (K.d i j ≫ Iso.inv K.rightUnitor' j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
Tactic: by_cases hij : c.Rel i j
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i j : I
pos :
  ∀ (hij : c.Rel i j),
    Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
      (Iso.inv K.rightUnitor' i ≫ (K.tensorObj (tensorUnit C c)).d i j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
      (K.d i j ≫ Iso.inv K.rightUnitor' j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
⊢ Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (Iso.inv K.rightUnitor' i ≫ (K.tensorObj (tensorUnit C c)).d i j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (K.d i j ≫ Iso.inv K.rightUnitor' j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
have neg : ∀ (hij : ¬c.Rel i j),
  Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (Iso.inv K.rightUnitor' i ≫ (K.tensorObj (tensorUnit C c)).d i j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (K.d i j ≫ Iso.inv K.rightUnitor' j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
Tactic: by_cases hij : c.Rel i j
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i j : I
hij : c.Rel i j
⊢ Eq.{v_1 + 1} (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (Iso.inv K.rightUnitor' i ≫ (K.tensorObj (tensorUnit C c)).d i j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (K.d i j ≫ Iso.inv K.rightUnitor' j : K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
have pos : Eq (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
  (Iso.inv (ρ_ (K.X i)) ≫
      K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
        mapBifunctor.d₁ K (tensorUnit C c) (curriedTensor C) c i 0 j :
    K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
  (K.d i j ≫
      Iso.inv (ρ_ (K.X j)) ≫
        K.X j ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
          K.ιTensorObj (tensorUnit C c) j 0 j sorry :
    K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
Tactic: simp only [rightUnitor'_inv, assoc, mapBifunctor.d_eq,
      Preadditive.comp_add, mapBifunctor.ι_D₁, mapBifunctor.ι_D₂,
      tensor_unit_d₂, comp_zero, add_zero]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Monoidal (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Preadditive.{v_1, u_1} C
inst_3 : HasZeroObject.{v_1, u_1} C
inst_4 : Functor.Additive (D := CategoryTheory.Functor.{v_1, v_1, u_1, u_1} C C) (curriedTensor C)
inst_5 : ∀ (X₁ : C), Functor.Additive.{v_1, u_1, v_1, u_1} (Functor.obj (curriedTensor C) X₁)
I : Type u_2
inst_6 : AddMonoid I
c : ComplexShape I
inst_7 : c.TensorSigns
K : HomologicalComplex.{v_1, u_1, u_2} C c
inst_8 : DecidableEq I
inst_9 : ∀ (X₁ : C), PreservesColimit.{0, 0, v_1, v_1, u_1, u_1} (Functor.empty C) (Functor.obj (curriedTensor C) X₁)
i j : I
hij : c.Rel i j
⊢ Eq (α := K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (Iso.inv (ρ_ (K.X i)) ≫
        K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
          mapBifunctor.d₁ K (tensorUnit C c) (curriedTensor C) c i 0 j :
      K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
    (K.d i j ≫
        Iso.inv (ρ_ (K.X j)) ≫
          K.X j ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
            K.ιTensorObj (tensorUnit C c) j 0 j ⋯ :
      K.X i ⟶ (K.tensorObj (tensorUnit C c)).X j)
have pos : Iso.inv (ρ_ (K.X i)) ≫
    K.X i ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
      HSMul.hSMul (β :=
        Functor.obj.{v_1, v_1, u_1, u_1} (Functor.obj (curriedTensor C) (K.X i))
            (X.{v_1, u_1, u_2} (tensorUnit C c) 0) ⟶
          X (K.mapBifunctor (tensorUnit C c) (curriedTensor C) c) j)
        (c.ε₁ c c (i, 0))
        (NatTrans.app (CategoryTheory.Functor.map (curriedTensor C) (K.d i j)) (X.{v_1, u_1, u_2} (tensorUnit C c) 0) ≫
          K.ιMapBifunctor (tensorUnit C c) (curriedTensor C) c j 0 j sorry) =
  K.d i j ≫
    Iso.inv (ρ_ (K.X j)) ≫
      K.X j ◁ Iso.inv (singleObjXSelf c 0 (MonoidalCategoryStruct.tensorUnit.{v_1, u_1} C (𝒞 := inst))) ≫
        K.ιTensorObj (tensorUnit C c) j 0 j sorry
Tactic: rw [mapBifunctor.d₁_eq _ _ _ _ hij _ _ (by simp)]