awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : ¬c₁₂.π c₃ c₄ (c₁₂.next i₁₂, i₃) = j'
h₃ : c₂.Rel i₂ (c₂.next i₂)
h₄ : c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂), i₃) = j'
pos : c₁₂.π c₃ c₄ (c₁₂.next i₁₂, i₃) = j'
⊢ False

Tactic:
apply h₂
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : ¬c₁₂.π c₃ c₄ (c₁₂.next i₁₂, i₃) = j'
h₃ : c₂.Rel i₂ (c₂.next i₂)
h₄ : c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂), i₃) = j'
pos : c₁₂.π c₃ c₄ (c₁₂.next i₁₂, i₃) = c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂), i₃)
pos₁ pos₂ : c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂), i₃) = c₁₂.π c₃ c₄ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂), i₃)
⊢ c₁₂.π c₃ c₄ (c₁₂.next i₁₂, i₃) = j'

Tactic:
rw [← h₄, ComplexShape.next_π₂ c₁ c₁₂ i₁ h₃]

Premises used: ComplexShape.next_π₂
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : ¬c₁₂.π c₃ c₄ (c₁₂.next i₁₂, i₃) = j'
h₃ : ¬c₂.Rel i₂ (c₂.next i₂)
neg neg₁ :
  Eq.{v_4 + 1} (α :=
    (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
      X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')
    0 0
⊢ Eq (α :=
    (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
      X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')
    (0 :
      (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
        X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')
    (d₂ F₁₂ G K₁ K₂ K₃ c₁₂ c₄ i₁ i₂ i₃ j' :
      (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
        X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')

Tactic:
rw [d₂_eq_zero _ _ _ _ _ _ _ _ _ _ _ h₃]

Premises used: HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
neg : ¬c₂.Rel i₂ (c₂.next i₂)
neg₁ : ¬c₁.Rel i₁ (c₁.next i₁)
⊢ NatTrans.app (G.map (K₁.ιMapBifunctor K₂ F₁₂ c₁₂ i₁ i₂ (c₁.π c₂ c₁₂ (i₁, i₂)) ⋯)) (K₃.X i₃) ≫
      mapBifunctor.d₁ (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄ (c₁.π c₂ c₁₂ (i₁, i₂)) i₃ j' =
    HAdd.hAdd (α :=
      (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
        X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')
      (β :=
      (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
        X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')
      (d₁ F₁₂ G K₁ K₂ K₃ c₁₂ c₄ i₁ i₂ i₃ j' :
        (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
          X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')
      (d₂ F₁₂ G K₁ K₂ K₃ c₁₂ c₄ i₁ i₂ i₃ j' :
        (G.obj ((F₁₂.obj (K₁.X i₁)).obj (K₂.X i₂))).obj (K₃.X i₃) ⟶
          X (mapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄) j')

Tactic:
rw [mapBifunctor.d₁_eq_zero _ _ _ _ _ _ _ h₁, comp_zero,
      d₁_eq_zero, d₂_eq_zero, zero_add]

Premises used: CategoryTheory.Limits.comp_zero, HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero, HomologicalComplex.mapBifunctor.d₁_eq_zero, zero_add, HomologicalComplex.mapBifunctor₁₂.d₁_eq_zero
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₂.Rel i₂ (c₂.next i₂)
neg : c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
⊢ False

Tactic:
apply h₁
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₂.Rel i₂ (c₂.next i₂)
⊢ c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))

Tactic:
have := ComplexShape.rel_π₂ c₁ c₁₂ i₁ h₂
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₂.Rel i₂ (c₂.next i₂)
this : c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))
neg : c₁₂.Rel i₁₂ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))
⊢ c₁₂.Rel i₁₂ (c₁₂.next i₁₂)

Tactic:
rw [c₁₂.next_eq' this]

Premises used: ComplexShape.next_eq'
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₂.Rel i₂ (c₂.next i₂)
this : c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))
⊢ c₁₂.Rel i₁₂ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))

Tactic:
this
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₂.Rel i₂ (c₂.next i₂)
this : c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))
⊢ c₁₂.Rel i₁₂ (c₁.π c₂ c₁₂ (i₁, c₂.next i₂))

Tactic:
exact this
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₁.Rel i₁ (c₁.next i₁)
neg : c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
⊢ False

Tactic:
apply h₁
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₁.Rel i₁ (c₁.next i₁)
⊢ c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (c₁.next i₁, i₂))

Tactic:
have := ComplexShape.rel_π₁ c₂ c₁₂ h₂ i₂
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₁.Rel i₁ (c₁.next i₁)
this : c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (c₁.next i₁, i₂))
neg : c₁₂.Rel i₁₂ (c₁.π c₂ c₁₂ (c₁.next i₁, i₂))
⊢ c₁₂.Rel i₁₂ (c₁₂.next i₁₂)

Tactic:
rw [c₁₂.next_eq' this]

Premises used: ComplexShape.next_eq'
-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₁₂ : Type u_3
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_5, u_3} C₁₂
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_5, u_3} C₁₂
inst_9 : Preadditive.{v_4, u_6} C₄
F₁₂ : C₁ ⥤ CategoryTheory.Functor.{v_2, v_5, u_2, u_3} C₂ C₁₂
G : C₁₂ ⥤ CategoryTheory.Functor.{v_3, v_4, u_5, u_6} C₃ C₄
inst_10 : F₁₂.PreservesZeroMorphisms
inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms
inst_12 : G.Additive
inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
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
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂
inst_18 : DecidableEq ι₁₂
inst_19 : HasMapBifunctor (K₁.mapBifunctor K₂ F₁₂ c₁₂) K₃ G c₄
j j' : ι₄
inst_20 : HasGoodTrifunctor₁₂Obj F₁₂ G K₁ K₂ K₃ c₁₂ c₄
i₁ : ι₁
i₂ : ι₂
i₃ : ι₃
h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j
i₁₂ : ι₁₂ := c₁.π c₂ c₁₂ (i₁, i₂)
h₁ : ¬c₁₂.Rel i₁₂ (c₁₂.next i₁₂)
h₂ : c₁.Rel i₁ (c₁.next i₁)
this : c₁₂.Rel (c₁.π c₂ c₁₂ (i₁, i₂)) (c₁.π c₂ c₁₂ (c₁.next i₁, i₂))
⊢ c₁₂.Rel i₁₂ (c₁.π c₂ c₁₂ (c₁.next i₁, i₂))

Tactic:
this