mathlib-initiative/mathlib-tactics huggingface dataset:
Module: Mathlib.Algebra.Homology.TotalComplexSymmetry

Goal state before:
pp: case pos
C : Type u_1
I₁ : Type u_2
I₂ : Type u_3
J : Type u_4
inst✝⁶ : Category.{v_1, u_1} C
inst✝⁵ : Preadditive C
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K : HomologicalComplex₂ C c₁ c₂
c : ComplexShape J
inst✝⁴ : TotalComplexShape c₁ c₂ c
inst✝³ : TotalComplexShape c₂ c₁ c
inst✝² : TotalComplexShapeSymmetry c₁ c₂ c
inst✝¹ : K.HasTotal c
inst✝ : DecidableEq J
j j' : J
h₀ : c.Rel j j'
i₂ : I₂
i₁ : I₁
h₁ : c₂.π c₁ c (i₂, i₁) = j
h₂ : c₁.Rel i₁ (c₁.next i₁)
h₃ : c₂.π c₁ c (i₂, c₁.next i₁) = j'
h₄ : c₁.π c₂ c (c₁.next i₁, i₂) = j'
⊢ c₁.σ c₂ c i₁ i₂ • c₁.ε₁ c₂ c (i₁, i₂) • (K.d i₁ (c₁.next i₁)).f i₂ ≫ K.ιTotal c (c₁.next i₁) i₂ j' h₄ =
    c₂.ε₂ c₁ c (i₂, i₁) •
      ((K.flip.X i₂).d i₁ (c₁.next i₁) ≫ K.flip.ιTotal c i₂ (c₁.next i₁) j' h₃) ≫
        K.flip.totalDesc fun i₂ i₁ h ↦ c₁.σ c₂ c i₁ i₂ • K.ιTotal c i₁ i₂ j' ⋯

Tactic:
assoc,

Goal state after:
case pos
C : Type u_1
I₁ : Type u_2
I₂ : Type u_3
J : Type u_4
inst✝⁶ : Category.{v_1, u_1} C
inst✝⁵ : Preadditive C
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K : HomologicalComplex₂ C c₁ c₂
c : ComplexShape J
inst✝⁴ : TotalComplexShape c₁ c₂ c
inst✝³ : TotalComplexShape c₂ c₁ c
inst✝² : TotalComplexShapeSymmetry c₁ c₂ c
inst✝¹ : K.HasTotal c
inst✝ : DecidableEq J
j j' : J
h₀ : c.Rel j j'
i₂ : I₂
i₁ : I₁
h₁ : c₂.π c₁ c (i₂, i₁) = j
h₂ : c₁.Rel i₁ (c₁.next i₁)
h₃ : c₂.π c₁ c (i₂, c₁.next i₁) = j'
h₄ : c₁.π c₂ c (c₁.next i₁, i₂) = j'
⊢ c₁.σ c₂ c i₁ i₂ • c₁.ε₁ c₂ c (i₁, i₂) • (K.d i₁ (c₁.next i₁)).f i₂ ≫ K.ιTotal c (c₁.next i₁) i₂ j' h₄ =
    c₂.ε₂ c₁ c (i₂, i₁) •
      (K.flip.X i₂).d i₁ (c₁.next i₁) ≫
        K.flip.ιTotal c i₂ (c₁.next i₁) j' h₃ ≫ K.flip.totalDesc fun i₂ i₁ h ↦ c₁.σ c₂ c i₁ i₂ • K.ιTotal c i₁ i₂ j' ⋯
Module: Mathlib.CategoryTheory.GradedObject.Trifunctor

Goal state before:
pp: C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₁₂ : Type u_5
C₂₃ : Type u_6
inst✝⁷ : Category.{v_1, u_1} C₁
inst✝⁶ : Category.{v_2, u_2} C₂
inst✝⁵ : Category.{v_3, u_3} C₃
inst✝⁴ : Category.{v_4, u_4} C₄
inst✝³ : Category.{v_5, u_5} C₁₂
inst✝² : Category.{v_6, u_6} C₂₃
F : C₁ ⥤ C₂₃ ⥤ C₄
G₂₃ : C₂ ⥤ C₃ ⥤ C₂₃
I₁ : Type u_7
I₂ : Type u_8
I₃ : Type u_9
J : Type u_10
r : I₁ × I₂ × I₃ → J
ρ₂₃ : BifunctorComp₂₃IndexData r
X₁ : GradedObject I₁ C₁
X₂ : GradedObject I₂ C₂
X₃ : GradedObject I₃ C₃
inst✝¹ : (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).HasMap ρ₂₃.p
inst✝ : (((mapBifunctor F I₁ ρ₂₃.I₂₃).obj X₁).obj (mapBifunctorMapObj G₂₃ ρ₂₃.p X₂ X₃)).HasMap ρ₂₃.q
H : HasGoodTrifunctor₂₃Obj F G₂₃ ρ₂₃ X₁ X₂ X₃
j : J
c₂₃ : (i₂₃ : ρ₂₃.I₂₃) → (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).CofanMapObjFun ρ₂₃.p i₂₃ :=
  fun i₂₃ ↦ (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).cofanMapObj ρ₂₃.p i₂₃
⊢ IsColimit (cofan₃MapBifunctorBifunctor₂₃MapObj F G₂₃ ρ₂₃ X₁ X₂ X₃ j)

Tactic:
have h₂₃ : ∀ i₂₃, IsColimit (c₂₃ i₂₃) := fun i₂₃ =>
    (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).isColimitCofanMapObj ρ₂₃.p i₂₃

Goal state after:
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₁₂ : Type u_5
C₂₃ : Type u_6
inst✝⁷ : Category.{v_1, u_1} C₁
inst✝⁶ : Category.{v_2, u_2} C₂
inst✝⁵ : Category.{v_3, u_3} C₃
inst✝⁴ : Category.{v_4, u_4} C₄
inst✝³ : Category.{v_5, u_5} C₁₂
inst✝² : Category.{v_6, u_6} C₂₃
F : C₁ ⥤ C₂₃ ⥤ C₄
G₂₃ : C₂ ⥤ C₃ ⥤ C₂₃
I₁ : Type u_7
I₂ : Type u_8
I₃ : Type u_9
J : Type u_10
r : I₁ × I₂ × I₃ → J
ρ₂₃ : BifunctorComp₂₃IndexData r
X₁ : GradedObject I₁ C₁
X₂ : GradedObject I₂ C₂
X₃ : GradedObject I₃ C₃
inst✝¹ : (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).HasMap ρ₂₃.p
inst✝ : (((mapBifunctor F I₁ ρ₂₃.I₂₃).obj X₁).obj (mapBifunctorMapObj G₂₃ ρ₂₃.p X₂ X₃)).HasMap ρ₂₃.q
H : HasGoodTrifunctor₂₃Obj F G₂₃ ρ₂₃ X₁ X₂ X₃
j : J
c₂₃ : (i₂₃ : ρ₂₃.I₂₃) → (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).CofanMapObjFun ρ₂₃.p i₂₃ :=
  fun i₂₃ ↦ (((mapBifunctor G₂₃ I₂ I₃).obj X₂).obj X₃).cofanMapObj ρ₂₃.p i₂₃
h₂₃ : (i₂₃ : ρ₂₃.I₂₃) → IsColimit (c₂₃ i₂₃)
⊢ IsColimit (cofan₃MapBifunctorBifunctor₂₃MapObj F G₂₃ ρ₂₃ X₁ X₂ X₃ j)
Module: Mathlib.Algebra.Homology.TotalComplexSymmetry

Goal state before:
pp: case pos
C : Type u_1
I₁ : Type u_2
I₂ : Type u_3
J : Type u_4
inst✝⁶ : Category.{v_1, u_1} C
inst✝⁵ : Preadditive C
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K : HomologicalComplex₂ C c₁ c₂
c : ComplexShape J
inst✝⁴ : TotalComplexShape c₁ c₂ c
inst✝³ : TotalComplexShape c₂ c₁ c
inst✝² : TotalComplexShapeSymmetry c₁ c₂ c
inst✝¹ : K.HasTotal c
inst✝ : DecidableEq J
j j' : J
h₀ : c.Rel j j'
i₂ : I₂
i₁ : I₁
h₁ : c₂.π c₁ c (i₂, i₁) = j
h₂ : c₂.Rel i₂ (c₂.next i₂)
h₃ : c₂.π c₁ c (c₂.next i₂, i₁) = j'
h₄ : c₁.π c₂ c (i₁, c₂.next i₂) = j'
⊢ c₁.σ c₂ c i₁ i₂ • c₁.ε₂ c₂ c (i₁, i₂) • (K.X i₁).d i₂ (c₂.next i₂) ≫ K.ιTotal c i₁ (c₂.next i₂) j' h₄ =
    c₂.ε₁ c₁ c (i₂, i₁) •
      ((K.flip.d i₂ (c₂.next i₂)).f i₁ ≫ K.flip.ιTotal c (c₂.next i₂) i₁ j' h₃) ≫
        K.flip.totalDesc fun i₂ i₁ h ↦ c₁.σ c₂ c i₁ i₂ • K.ιTotal c i₁ i₂ j' ⋯

Tactic:
assoc,

Goal state after:
case pos
C : Type u_1
I₁ : Type u_2
I₂ : Type u_3
J : Type u_4
inst✝⁶ : Category.{v_1, u_1} C
inst✝⁵ : Preadditive C
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K : HomologicalComplex₂ C c₁ c₂
c : ComplexShape J
inst✝⁴ : TotalComplexShape c₁ c₂ c
inst✝³ : TotalComplexShape c₂ c₁ c
inst✝² : TotalComplexShapeSymmetry c₁ c₂ c
inst✝¹ : K.HasTotal c
inst✝ : DecidableEq J
j j' : J
h₀ : c.Rel j j'
i₂ : I₂
i₁ : I₁
h₁ : c₂.π c₁ c (i₂, i₁) = j
h₂ : c₂.Rel i₂ (c₂.next i₂)
h₃ : c₂.π c₁ c (c₂.next i₂, i₁) = j'
h₄ : c₁.π c₂ c (i₁, c₂.next i₂) = j'
⊢ c₁.σ c₂ c i₁ i₂ • c₁.ε₂ c₂ c (i₁, i₂) • (K.X i₁).d i₂ (c₂.next i₂) ≫ K.ιTotal c i₁ (c₂.next i₂) j' h₄ =
    c₂.ε₁ c₁ c (i₂, i₁) •
      (K.flip.d i₂ (c₂.next i₂)).f i₁ ≫
        K.flip.ιTotal c (c₂.next i₂) i₁ j' h₃ ≫ K.flip.totalDesc fun i₂ i₁ h ↦ c₁.σ c₂ c i₁ i₂ • K.ιTotal c i₁ i₂ j' ⋯
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
i₁ i₁' : I₁
hi₁ : c₁.Rel i₁ i₁'
i₂ i₂' : I₂
hi₂ : c₂.Rel i₂ i₂'
j : J
hj : c₁.π c₂ c (i₁', i₂) = j
hj' : c₁.π c₂ c (i₁, i₂') = j
⊢ c₁.ε₁ c₂ c (i₁, i₂) •
      c₁.ε₂ c₂ c (i₁, i₂) •
        (F.map (h₁.hom i₁' i₁)).app (K₂.X i₂) ≫
          (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫
            ((((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).X i₁).d i₂ i₂' ≫
              (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).ιTotal c i₁ i₂' j hj' =
    -(c₁.ε₂ c₂ c (i₁', i₂) •
        (((((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).X i₁').d i₂ i₂' ≫
            (((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).ιTotal c i₁' i₂' (c.next j) ⋯) ≫
          hom₁ h₁ f₂ F c (c.next j) j)

Tactic:
assoc,

Goal state after:
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
i₁ i₁' : I₁
hi₁ : c₁.Rel i₁ i₁'
i₂ i₂' : I₂
hi₂ : c₂.Rel i₂ i₂'
j : J
hj : c₁.π c₂ c (i₁', i₂) = j
hj' : c₁.π c₂ c (i₁, i₂') = j
⊢ c₁.ε₁ c₂ c (i₁, i₂) •
      c₁.ε₂ c₂ c (i₁, i₂) •
        (F.map (h₁.hom i₁' i₁)).app (K₂.X i₂) ≫
          (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫
            ((((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).X i₁).d i₂ i₂' ≫
              (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).ιTotal c i₁ i₂' j hj' =
    -(c₁.ε₂ c₂ c (i₁', i₂) •
        ((((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).X i₁').d i₂ i₂' ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).ιTotal c i₁' i₂' (c.next j) ⋯ ≫
            hom₁ h₁ f₂ F c (c.next j) j)
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel i₁ (c₁.next i₁)
⊢ (F.map (K₁.d i₁ (c₁.next i₁))).app (K₂.X i₂) ≫
      (F.map (h₁.hom (c₁.next i₁) i₁)).app (K₂.X i₂) ≫
        (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c i₁ i₂ j h =
    c₁.ε₁ c₂ c (i₁, i₂) •
      ((F.map (K₁.d i₁ (c₁.next i₁))).app (K₂.X i₂) ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).ιTotal c (c₁.next i₁) i₂ (c.next j) ⋯) ≫
        hom₁ h₁ f₂ F c (c.next j) j

Tactic:
assoc,

Goal state after:
case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel i₁ (c₁.next i₁)
⊢ (F.map (K₁.d i₁ (c₁.next i₁))).app (K₂.X i₂) ≫
      (F.map (h₁.hom (c₁.next i₁) i₁)).app (K₂.X i₂) ≫
        (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c i₁ i₂ j h =
    c₁.ε₁ c₂ c (i₁, i₂) •
      (F.map (K₁.d i₁ (c₁.next i₁))).app (K₂.X i₂) ≫
        (((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).ιTotal c (c₁.next i₁) i₂ (c.next j) ⋯ ≫
          hom₁ h₁ f₂ F c (c.next j) j
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
      (F.map (L₁.d (c₁.prev i₁) i₁)).app (K₂.X i₂) ≫
        (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c i₁ i₂ j h =
    c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      ((F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
          (F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c (c₁.prev i₁) i₂ (c.prev j) ⋯) ≫
        (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₁ c (c.prev j) j

Tactic:
assoc,

Goal state after:
case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
      (F.map (L₁.d (c₁.prev i₁) i₁)).app (K₂.X i₂) ≫
        (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c i₁ i₂ j h =
    c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
        ((F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c (c₁.prev i₁) i₂ (c.prev j) ⋯) ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₁ c (c.prev j) j
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
      (F.map (L₁.d (c₁.prev i₁) i₁)).app (K₂.X i₂) ≫
        (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c i₁ i₂ j h =
    c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
        ((F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c (c₁.prev i₁) i₂ (c.prev j) ⋯) ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₁ c (c.prev j) j

Tactic:
assoc,

Goal state after:
case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
      (F.map (L₁.d (c₁.prev i₁) i₁)).app (K₂.X i₂) ≫
        (F.obj (L₁.X i₁)).map (f₂.f i₂) ≫ L₁.ιMapBifunctor L₂ F c i₁ i₂ j h =
    c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
        (F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫
          L₁.ιMapBifunctor L₂ F c (c₁.prev i₁) i₂ (c.prev j) ⋯ ≫
            (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₁ c (c.prev j) j
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      ((F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
          (F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫ L₁.ιMapBifunctorOrZero L₂ F c (c₁.prev i₁) i₂ (c.prev j)) ≫
        (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₂ c (c.prev j) j =
    -(((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).d₂ c i₁ i₂ (c.next j) ≫ hom₁ h₁ f₂ F c (c.next j) j

Tactic:
assoc,

Goal state after:
case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
        ((F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫ L₁.ιMapBifunctorOrZero L₂ F c (c₁.prev i₁) i₂ (c.prev j)) ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₂ c (c.prev j) j =
    -(((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).d₂ c i₁ i₂ (c.next j) ≫ hom₁ h₁ f₂ F c (c.next j) j
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
        ((F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫ L₁.ιMapBifunctorOrZero L₂ F c (c₁.prev i₁) i₂ (c.prev j)) ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₂ c (c.prev j) j =
    -(((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).d₂ c i₁ i₂ (c.next j) ≫ hom₁ h₁ f₂ F c (c.next j) j

Tactic:
assoc,

Goal state after:
case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : c₁.Rel (c₁.prev i₁) i₁
⊢ c₁.ε₁ c₂ c (c₁.prev i₁, i₂) •
      (F.map (h₁.hom i₁ (c₁.prev i₁))).app (K₂.X i₂) ≫
        (F.obj (L₁.X (c₁.prev i₁))).map (f₂.f i₂) ≫
          L₁.ιMapBifunctorOrZero L₂ F c (c₁.prev i₁) i₂ (c.prev j) ≫
            (((F.mapBifunctorHomologicalComplex c₁ c₂).obj L₁).obj L₂).D₂ c (c.prev j) j =
    -(((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).d₂ c i₁ i₂ (c.next j) ≫ hom₁ h₁ f₂ F c (c.next j) j
Module: Mathlib.Algebra.Homology.BifunctorHomotopy

Goal state before:
pp: case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : ¬c₁.Rel (c₁.prev i₁) i₁
h₄ : c₂.Rel i₂ (c₂.next i₂)
h₅ : c.Rel j (c.next j)
⊢ c₁.ε₂ c₂ c (i₁, i₂) •
      (((((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).X i₁).d i₂ (c₂.next i₂) ≫
          (((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).ιTotal c i₁ (c₂.next i₂) (c.next j) ⋯) ≫
        hom₁ h₁ f₂ F c (c.next j) j =
    0

Tactic:
assoc,

Goal state after:
case pos
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
I₁ : Type u_4
I₂ : Type u_5
J : Type u_6
inst✝¹¹ : Category.{v_1, u_1} C₁
inst✝¹⁰ : Category.{v_2, u_2} C₂
inst✝⁹ : Category.{v_3, u_3} D
inst✝⁸ : Preadditive C₁
inst✝⁷ : Preadditive C₂
inst✝⁶ : Preadditive D
c₁ : ComplexShape I₁
c₂ : ComplexShape I₂
K₁ L₁ : HomologicalComplex C₁ c₁
f₁ f₁' : K₁ ⟶ L₁
h₁ : Homotopy f₁ f₁'
K₂ L₂ : HomologicalComplex C₂ c₂
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ C₂ ⥤ D
inst✝⁵ : F.Additive
inst✝⁴ : ∀ (X₁ : C₁), (F.obj X₁).Additive
c : ComplexShape J
inst✝³ : DecidableEq J
inst✝² : TotalComplexShape c₁ c₂ c
inst✝¹ : K₁.HasMapBifunctor K₂ F c
inst✝ : L₁.HasMapBifunctor L₂ F c
j : J
i₁ : I₁
i₂ : I₂
h : c₁.π c₂ c (i₁, i₂) = j
this : ∀ {X Y : D} (a b c d e f : X ⟶ Y), a = c → b = e → f = -d → a + b = c + d + (e + f)
h₃ : ¬c₁.Rel (c₁.prev i₁) i₁
h₄ : c₂.Rel i₂ (c₂.next i₂)
h₅ : c.Rel j (c.next j)
⊢ c₁.ε₂ c₂ c (i₁, i₂) •
      ((((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).X i₁).d i₂ (c₂.next i₂) ≫
        (((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂).ιTotal c i₁ (c₂.next i₂) (c.next j) ⋯ ≫
          hom₁ h₁ f₂ F c (c.next j) j =
    0