mathlib-initiative/mathlib-tactics huggingface dataset:
Module: Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence

Goal state before:
pp: case refine_1
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
q : ℕ
⊢ P (q + 1) = P q + P q ≫ Hσ q

pp: case refine_2
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
q : ℕ
⊢ 𝟙 K[X] + P q ≫ 0 = 𝟙 K[X]

Tactic:
·

Goal state after:
case refine_1
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
q : ℕ
⊢ P (q + 1) = P q + P q ≫ Hσ q
Module: Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence

Goal state before:
pp: case refine_2
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
q : ℕ
⊢ 𝟙 K[X] + P q ≫ 0 = 𝟙 K[X]

Tactic:
·

Goal state after:
case refine_2
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
q : ℕ
⊢ 𝟙 K[X] + P q ≫ 0 = 𝟙 K[X]
Module: Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence

Goal state before:
pp: case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
⊢ PInfty.f 0 =
    (((dNext 0) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) + (prevD 0) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
      (𝟙 K[X]).f 0

pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
⊢ PInfty.f (n + 1) =
    (((dNext (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
        (prevD (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
      (𝟙 K[X]).f (n + 1)

Tactic:
·

Goal state after:
case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
⊢ PInfty.f 0 =
    (((dNext 0) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) + (prevD 0) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
      (𝟙 K[X]).f 0
Module: Mathlib.AlgebraicTopology.DoldKan.Normalized

Goal state before:
pp: case zero
A : Type u_1
inst✝¹ : Category.{v_1, u_1} A
inst✝ : Abelian A
X : SimplicialObject A
⊢ (inclusionOfMooreComplexMap X ≫ PInfty).f 0 = (inclusionOfMooreComplexMap X).f 0

pp: case succ
A : Type u_1
inst✝¹ : Category.{v_1, u_1} A
inst✝ : Abelian A
X : SimplicialObject A
n : ℕ
⊢ (inclusionOfMooreComplexMap X ≫ PInfty).f (n + 1) = (inclusionOfMooreComplexMap X).f (n + 1)

Tactic:
·

Goal state after:
case zero
A : Type u_1
inst✝¹ : Category.{v_1, u_1} A
inst✝ : Abelian A
X : SimplicialObject A
⊢ (inclusionOfMooreComplexMap X ≫ PInfty).f 0 = (inclusionOfMooreComplexMap X).f 0
Module: Mathlib.AlgebraicTopology.DoldKan.Normalized

Goal state before:
pp: case succ
A : Type u_1
inst✝¹ : Category.{v_1, u_1} A
inst✝ : Abelian A
X : SimplicialObject A
n : ℕ
⊢ (inclusionOfMooreComplexMap X ≫ PInfty).f (n + 1) = (inclusionOfMooreComplexMap X).f (n + 1)

Tactic:
·

Goal state after:
case succ
A : Type u_1
inst✝¹ : Category.{v_1, u_1} A
inst✝ : Abelian A
X : SimplicialObject A
n : ℕ
⊢ (inclusionOfMooreComplexMap X ≫ PInfty).f (n + 1) = (inclusionOfMooreComplexMap X).f (n + 1)
Module: Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence

Goal state before:
pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
⊢ PInfty.f (n + 1) =
    (((dNext (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
        (prevD (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
      (𝟙 K[X]).f (n + 1)

Tactic:
·

Goal state after:
case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
⊢ PInfty.f (n + 1) =
    (((dNext (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
        (prevD (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +
      (𝟙 K[X]).f (n + 1)
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T U : C
g : T ⟶ U
f : X _⦋0⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ DegeneraciesVanish (f ≫ g)

pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T U : C
g : T ⟶ U
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ DegeneraciesVanish (f ≫ g)

Tactic:
·

Goal state after:
case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T U : C
g : T ⟶ U
f : X _⦋0⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ DegeneraciesVanish (f ≫ g)
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T U : C
g : T ⟶ U
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ DegeneraciesVanish (f ≫ g)

Tactic:
·

Goal state after:
case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T U : C
g : T ⟶ U
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ DegeneraciesVanish (f ≫ g)
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
⊢ DegeneraciesVanish (PInfty.f 0)

pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
⊢ DegeneraciesVanish (PInfty.f (n + 1))

Tactic:
·

Goal state after:
case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
⊢ DegeneraciesVanish (PInfty.f 0)
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
⊢ DegeneraciesVanish (PInfty.f (n + 1))

Tactic:
·

Goal state after:
case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
⊢ DegeneraciesVanish (PInfty.f (n + 1))
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
f : X _⦋0⦌ ⟶ T
⊢ DegeneraciesVanish f ↔ QInfty.f 0 ≫ f = 0

pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
⊢ DegeneraciesVanish f ↔ QInfty.f (n + 1) ≫ f = 0

Tactic:
·

Goal state after:
case zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
f : X _⦋0⦌ ⟶ T
⊢ DegeneraciesVanish f ↔ QInfty.f 0 ≫ f = 0
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
⊢ DegeneraciesVanish f ↔ QInfty.f (n + 1) ≫ f = 0

Tactic:
·

Goal state after:
case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
⊢ DegeneraciesVanish f ↔ QInfty.f (n + 1) ≫ f = 0
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case succ.refine_1
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ QInfty.f (n + 1) ≫ f = 0

pp: case succ.refine_2
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : QInfty.f (n + 1) ≫ f = 0
⊢ DegeneraciesVanish f

Tactic:
·

Goal state after:
case succ.refine_1
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : DegeneraciesVanish f
⊢ QInfty.f (n + 1) ≫ f = 0
Module: Mathlib.AlgebraicTopology.DoldKan.Degeneracies

Goal state before:
pp: case succ.refine_2
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : QInfty.f (n + 1) ≫ f = 0
⊢ DegeneraciesVanish f

Tactic:
·

Goal state after:
case succ.refine_2
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
T : C
n : ℕ
f : X _⦋n + 1⦌ ⟶ T
hf : QInfty.f (n + 1) ≫ f = 0
⊢ DegeneraciesVanish f
Module: Mathlib.AlgebraicTopology.DoldKan.GammaCompN

Goal state before:
pp: C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ K.d (n + 1) n =
    ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      ((-1) ^ ↑0 • (Γ₀.obj K).δ 0) ≫ (Γ₀.splitting K).πSummand (Splitting.IndexSet.id (op ⦋n⦌))

pp: C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ ∀ (x : Fin (n + 2)),
    x ≠ 0 →
      ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
          ((-1) ^ ↑x • (Γ₀.obj K).δ x) ≫ (Γ₀.splitting K).πSummand (Splitting.IndexSet.id (op ⦋n⦌)) =
        0

Tactic:
·

Goal state after:
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ K.d (n + 1) n =
    ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      ((-1) ^ ↑0 • (Γ₀.obj K).δ 0) ≫ (Γ₀.splitting K).πSummand (Splitting.IndexSet.id (op ⦋n⦌))
Module: Mathlib.AlgebraicTopology.DoldKan.GammaCompN

Goal state before:
pp: C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ ∀ (x : Fin (n + 2)),
    x ≠ 0 →
      ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
          ((-1) ^ ↑x • (Γ₀.obj K).δ x) ≫ (Γ₀.splitting K).πSummand (Splitting.IndexSet.id (op ⦋n⦌)) =
        0

Tactic:
·

Goal state after:
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ ∀ (x : Fin (n + 2)),
    x ≠ 0 →
      ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
          ((-1) ^ ↑x • (Γ₀.obj K).δ x) ≫ (Γ₀.splitting K).πSummand (Splitting.IndexSet.id (op ⦋n⦌)) =
        0
Module: Mathlib.AlgebraicTopology.DoldKan.GammaCompN

Goal state before:
pp: case h₁
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
i : Fin (n + 2)
hi : i ≠ 0
⊢ ⦋n + 1⦌ ≠ ⦋n⦌

pp: case h₂
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
i : Fin (n + 2)
hi : i ≠ 0
⊢ ¬Isδ₀ (SimplexCategory.δ i)

Tactic:
·

Goal state after:
case h₁
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
i : Fin (n + 2)
hi : i ≠ 0
⊢ ⦋n + 1⦌ ≠ ⦋n⦌
Module: Mathlib.AlgebraicTopology.DoldKan.GammaCompN

Goal state before:
pp: case h₂
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
i : Fin (n + 2)
hi : i ≠ 0
⊢ ¬Isδ₀ (SimplexCategory.δ i)

Tactic:
·

Goal state after:
case h₂
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
i : Fin (n + 2)
hi : i ≠ 0
⊢ ¬Isδ₀ (SimplexCategory.δ i)
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : HasZeroMorphisms C
Δ : SimplexCategoryᵒᵖ
A B : IndexSet Δ
h : B = A
⊢ s.N (unop B.fst).len ⟶ s.N (unop A.fst).len

pp: case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : HasZeroMorphisms C
Δ : SimplexCategoryᵒᵖ
A B : IndexSet Δ
h : ¬B = A
⊢ s.N (unop B.fst).len ⟶ s.N (unop A.fst).len

Tactic:
·

Goal state after:
case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : HasZeroMorphisms C
Δ : SimplexCategoryᵒᵖ
A B : IndexSet Δ
h : B = A
⊢ s.N (unop B.fst).len ⟶ s.N (unop A.fst).len
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : HasZeroMorphisms C
Δ : SimplexCategoryᵒᵖ
A B : IndexSet Δ
h : ¬B = A
⊢ s.N (unop B.fst).len ⟶ s.N (unop A.fst).len

Tactic:
·

Goal state after:
case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : HasZeroMorphisms C
Δ : SimplexCategoryᵒᵖ
A B : IndexSet Δ
h : ¬B = A
⊢ s.N (unop B.fst).len ⟶ s.N (unop A.fst).len
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case h₀
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Δ : SimplexCategoryᵒᵖ
A : IndexSet Δ
⊢ ∀ b ∈ Finset.univ, b ≠ A → (s.cofan Δ).inj A ≫ s.πSummand b ≫ (s.cofan Δ).inj b = 0

pp: case h₁
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Δ : SimplexCategoryᵒᵖ
A : IndexSet Δ
⊢ A ∉ Finset.univ → (s.cofan Δ).inj A ≫ s.πSummand A ≫ (s.cofan Δ).inj A = 0

Tactic:
·

Goal state after:
case h₀
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Δ : SimplexCategoryᵒᵖ
A : IndexSet Δ
⊢ ∀ b ∈ Finset.univ, b ≠ A → (s.cofan Δ).inj A ≫ s.πSummand b ≫ (s.cofan Δ).inj b = 0
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case h₁
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Δ : SimplexCategoryᵒᵖ
A : IndexSet Δ
⊢ A ∉ Finset.univ → (s.cofan Δ).inj A ≫ s.πSummand A ≫ (s.cofan Δ).inj A = 0

Tactic:
·

Goal state after:
case h₁
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Δ : SimplexCategoryᵒᵖ
A : IndexSet Δ
⊢ A ∉ Finset.univ → (s.cofan Δ).inj A ≫ s.πSummand A ≫ (s.cofan Δ).inj A = 0
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case mp
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
⊢ f ≫ PInfty.f n = 0 → f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0

pp: case mpr
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0 → f ≫ PInfty.f n = 0

Tactic:
·

Goal state after:
case mp
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
⊢ f ≫ PInfty.f n = 0 → f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case mp.zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
f : Z ⟶ X _⦋0⦌
h : f ≫ PInfty.f 0 = 0
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋0⦌)) = 0

pp: case mp.succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n + 1⦌
h : f ≫ PInfty.f (n + 1) = 0
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋n + 1⦌)) = 0

Tactic:
·

Goal state after:
case mp.zero
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
f : Z ⟶ X _⦋0⦌
h : f ≫ PInfty.f 0 = 0
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋0⦌)) = 0
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case mp.succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n + 1⦌
h : f ≫ PInfty.f (n + 1) = 0
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋n + 1⦌)) = 0

Tactic:
·

Goal state after:
case mp.succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n + 1⦌
h : f ≫ PInfty.f (n + 1) = 0
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋n + 1⦌)) = 0
Module: Mathlib.AlgebraicTopology.DoldKan.FunctorGamma

Goal state before:
pp: case h₁
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    Γ₀.Obj.Termwise.mapMono K (SimplexCategory.δ j.succ) ≫
      ((Γ₀.splitting K).cofan (op ⦋n⦌)).inj (Splitting.IndexSet.id (op ⦋n⦌))
⊢ ⦋n + 1⦌ ≠ ⦋n⦌

pp: case h₂
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    Γ₀.Obj.Termwise.mapMono K (SimplexCategory.δ j.succ) ≫
      ((Γ₀.splitting K).cofan (op ⦋n⦌)).inj (Splitting.IndexSet.id (op ⦋n⦌))
⊢ ¬Isδ₀ (SimplexCategory.δ j.succ)

pp: C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    0
⊢ ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫ (Γ₀.obj K).δ j.succ = 0

Tactic:
·

Goal state after:
case h₁
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    Γ₀.Obj.Termwise.mapMono K (SimplexCategory.δ j.succ) ≫
      ((Γ₀.splitting K).cofan (op ⦋n⦌)).inj (Splitting.IndexSet.id (op ⦋n⦌))
⊢ ⦋n + 1⦌ ≠ ⦋n⦌
Module: Mathlib.AlgebraicTopology.DoldKan.FunctorGamma

Goal state before:
pp: case h₂
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    Γ₀.Obj.Termwise.mapMono K (SimplexCategory.δ j.succ) ≫
      ((Γ₀.splitting K).cofan (op ⦋n⦌)).inj (Splitting.IndexSet.id (op ⦋n⦌))
⊢ ¬Isδ₀ (SimplexCategory.δ j.succ)

pp: C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    0
⊢ ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫ (Γ₀.obj K).δ j.succ = 0

Tactic:
·

Goal state after:
case h₂
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
j : Fin (n + 1)
a✝ : n + 1 ≤ ↑j + (n + 1)
eq :
  ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫
      (Γ₀.obj K).map (SimplexCategory.δ j.succ).op =
    Γ₀.Obj.Termwise.mapMono K (SimplexCategory.δ j.succ) ≫
      ((Γ₀.splitting K).cofan (op ⦋n⦌)).inj (Splitting.IndexSet.id (op ⦋n⦌))
⊢ ¬Isδ₀ (SimplexCategory.δ j.succ)
Module: Mathlib.AlgebraicTopology.DoldKan.FunctorGamma

Goal state before:
pp: case zero
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
⊢ ((Γ₀.splitting K).cofan (op ⦋0⦌)).inj (Splitting.IndexSet.id (op ⦋0⦌)) ≫ (P 0).f 0 =
    ((Γ₀.splitting K).cofan (op ⦋0⦌)).inj (Splitting.IndexSet.id (op ⦋0⦌))

pp: case succ
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫ (P (n + 1)).f (n + 1) =
    ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌))

Tactic:
·

Goal state after:
case zero
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
⊢ ((Γ₀.splitting K).cofan (op ⦋0⦌)).inj (Splitting.IndexSet.id (op ⦋0⦌)) ≫ (P 0).f 0 =
    ((Γ₀.splitting K).cofan (op ⦋0⦌)).inj (Splitting.IndexSet.id (op ⦋0⦌))
Module: Mathlib.AlgebraicTopology.DoldKan.FunctorGamma

Goal state before:
pp: case succ
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫ (P (n + 1)).f (n + 1) =
    ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌))

Tactic:
·

Goal state after:
case succ
C : Type u_1
inst✝² : Category.{v_1, u_1} C
inst✝¹ : Preadditive C
inst✝ : HasFiniteCoproducts C
K : ChainComplex C ℕ
n : ℕ
⊢ ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫ (P (n + 1)).f (n + 1) =
    ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌))
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case mpr
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0 → f ≫ PInfty.f n = 0

Tactic:
·

Goal state after:
case mpr
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
⊢ f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0 → f ≫ PInfty.f n = 0
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
h : f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0
A : IndexSet (op ⦋n⦌)
hA : A.EqId
⊢ f ≫ (s.πSummand A ≫ (s.cofan (op ⦋n⦌)).inj A) ≫ PInfty.f n = 0

pp: case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
h : f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0
A : IndexSet (op ⦋n⦌)
hA : ¬A.EqId
⊢ f ≫ (s.πSummand A ≫ (s.cofan (op ⦋n⦌)).inj A) ≫ PInfty.f n = 0

Tactic:
·

Goal state after:
case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
h : f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0
A : IndexSet (op ⦋n⦌)
hA : A.EqId
⊢ f ≫ (s.πSummand A ≫ (s.cofan (op ⦋n⦌)).inj A) ≫ PInfty.f n = 0
Module: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Goal state before:
pp: case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
h : f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0
A : IndexSet (op ⦋n⦌)
hA : ¬A.EqId
⊢ f ≫ (s.πSummand A ≫ (s.cofan (op ⦋n⦌)).inj A) ≫ PInfty.f n = 0

Tactic:
·

Goal state after:
case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
X : SimplicialObject C
s : X.Splitting
inst✝ : Preadditive C
Z : C
n : ℕ
f : Z ⟶ X _⦋n⦌
h : f ≫ s.πSummand (IndexSet.id (op ⦋n⦌)) = 0
A : IndexSet (op ⦋n⦌)
hA : ¬A.EqId
⊢ f ≫ (s.πSummand A ≫ (s.cofan (op ⦋n⦌)).inj A) ≫ PInfty.f n = 0