awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ i₁' : ι₁
h₁ : c₁.Rel i₁ i₁'
i₂ : ι₂
i₃ : ι₃
j : ι₄
obtain :
  ∀ (h₁ : c₁.Rel i₁ (c₁.next i₁)),
    d₁ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
      HSMul.hSMul (β :=
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
        (c₁.ε₁ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)))
        (CategoryStruct.comp (Y := (F.obj (K₁.X (c₁.next i₁))).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)))
            (NatTrans.app (F.map (K₁.d i₁ (c₁.next i₁))) ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)))
            (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ (c₁.next i₁) i₂ i₃ j) :
          (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
⊢ d₁ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
    HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₁ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)))
      ((F.map (K₁.d i₁ i₁')).app ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ≫ ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁' i₂ i₃ j :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
obtain rfl := c₁.next_eq' h₁

Premises used: rfl, ComplexShape.next_eq'
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j : ι₄
h₁ : c₁.Rel i₁ (c₁.next i₁)
⊢ d₁ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
    HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₁ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)))
      (CategoryStruct.comp (Y := (F.obj (K₁.X (c₁.next i₁))).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)))
          (NatTrans.app (F.map (K₁.d i₁ (c₁.next i₁))) ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)))
          (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ (c₁.next i₁) i₂ i₃ j) :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
rfl
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j : ι₄
h : ¬c₂.Rel i₂ (c₂.next i₂)
dsimp :
  HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₁ c₃ c₂₃ (i₂, i₃))
      (CategoryStruct.comp (Y := (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X (c₂.next i₂))).obj (K₃.X i₃)))
          ((F.obj (K₁.X i₁)).map (NatTrans.app (G₂₃.map (K₂.d i₂ (c₂.next i₂))) (K₃.X i₃)))
          (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ (c₂.next i₂) i₃ j) :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j) =
    0
⊢ Eq (α :=
    (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶ X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
    (d₂ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j :
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
    (0 :
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
dsimp [d₂]

Premises used: HomologicalComplex.mapBifunctor₂₃.d₂
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ i₂' : ι₂
h₂ : c₂.Rel i₂ i₂'
i₃ : ι₃
j : ι₄
obtain :
  ∀ (h₂ : c₂.Rel i₂ (c₂.next i₂)),
    d₂ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
      HSMul.hSMul (β :=
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
        (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₁ c₃ c₂₃ (i₂, i₃))
        (CategoryStruct.comp (Y := (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X (c₂.next i₂))).obj (K₃.X i₃)))
            ((F.obj (K₁.X i₁)).map (NatTrans.app (G₂₃.map (K₂.d i₂ (c₂.next i₂))) (K₃.X i₃)))
            (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ (c₂.next i₂) i₃ j) :
          (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
⊢ d₂ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
    HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₁ c₃ c₂₃ (i₂, i₃))
      ((F.obj (K₁.X i₁)).map ((G₂₃.map (K₂.d i₂ i₂')).app (K₃.X i₃)) ≫ ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂' i₃ j :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
obtain rfl := c₂.next_eq' h₂

Premises used: rfl, ComplexShape.next_eq'
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j : ι₄
h₂ : c₂.Rel i₂ (c₂.next i₂)
⊢ d₂ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
    HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₁ c₃ c₂₃ (i₂, i₃))
      (CategoryStruct.comp (Y := (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X (c₂.next i₂))).obj (K₃.X i₃)))
          ((F.obj (K₁.X i₁)).map (NatTrans.app (G₂₃.map (K₂.d i₂ (c₂.next i₂))) (K₃.X i₃)))
          (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ (c₂.next i₂) i₃ j) :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
rfl
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j : ι₄
h : ¬c₃.Rel i₃ (c₃.next i₃)
dsimp :
  HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₂ c₃ c₂₃ (i₂, i₃))
      (CategoryStruct.comp (Y := (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X (c₃.next i₃))))
          ((F.obj (K₁.X i₁)).map ((G₂₃.obj (K₂.X i₂)).map (K₃.d i₃ (c₃.next i₃))))
          (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ (c₃.next i₃) j) :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j) =
    0
⊢ Eq (α :=
    (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶ X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
    (d₃ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j :
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
    (0 :
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
dsimp [d₃]

Premises used: HomologicalComplex.mapBifunctor₂₃.d₃
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ i₃' : ι₃
h₃ : c₃.Rel i₃ i₃'
j : ι₄
obtain :
  ∀ (h₃ : c₃.Rel i₃ (c₃.next i₃)),
    d₃ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
      HSMul.hSMul (β :=
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
        (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₂ c₃ c₂₃ (i₂, i₃))
        (CategoryStruct.comp (Y := (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X (c₃.next i₃))))
            ((F.obj (K₁.X i₁)).map ((G₂₃.obj (K₂.X i₂)).map (K₃.d i₃ (c₃.next i₃))))
            (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ (c₃.next i₃) j) :
          (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
⊢ d₃ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
    HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₂ c₃ c₂₃ (i₂, i₃))
      ((F.obj (K₁.X i₁)).map ((G₂₃.obj (K₂.X i₂)).map (K₃.d i₃ i₃')) ≫ ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃' j :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
obtain rfl := c₃.next_eq' h₃

Premises used: rfl, ComplexShape.next_eq'
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j : ι₄
h₃ : c₃.Rel i₃ (c₃.next i₃)
⊢ d₃ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j =
    HSMul.hSMul (β :=
      (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
      (c₁.ε₂ c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) * c₂.ε₂ c₃ c₂₃ (i₂, i₃))
      (CategoryStruct.comp (Y := (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X (c₃.next i₃))))
          ((F.obj (K₁.X i₁)).map ((G₂₃.obj (K₂.X i₂)).map (K₃.d i₃ (c₃.next i₃))))
          (ιOrZero F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ (c₃.next i₃) j) :
        (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)

Tactic:
rfl
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j j' : ι₄
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
rw : c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, i₂), i₃) = c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃)
⊢ c₁.π c₂₃ c₄ (i₁, c₂.π c₃ c₂₃ (i₂, i₃)) = j

Tactic:
rw [← h, ← ComplexShape.assoc c₁ c₂ c₃ c₁₂ c₂₃ c₄]

Premises used: ComplexShape.assoc
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
j j' : ι₄
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
⊢ c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, i₂), i₃) = c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃)

Tactic:
rfl