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

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a✝ q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a✝ + q
hnaq_shift : ∀ (d : ℕ), n + d = a✝ + d + q
a b c d e f : Y ⟶ X _⦋n + 1⦌
h1 : b = f
h2 : d + e = 0
h3 : c + a = 0
⊢ f = f

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 + z2‖ < ‖z2‖
hne : ¬‖z1‖ = ‖z2‖
⊢ ‖z2‖ ≤ max ‖z1‖ ‖z2‖

Tactic:
]

Goal state after:
p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 + z2‖ < ‖z2‖
hne : ¬‖z1‖ = ‖z2‖
⊢ ‖z2‖ ≤ max ‖z1‖ ‖z2‖
Module: Mathlib.AlgebraicTopology.DoldKan.Projections

Goal state before:
pp: case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X x✝¹ x✝ : SimplicialObject C
f : x✝¹ ⟶ x✝
q : ℕ
hq : (alternatingFaceMapComplex C).map f ≫ P q = P q ≫ (alternatingFaceMapComplex C).map f
⊢ P q ≫ (alternatingFaceMapComplex C).map f + P q ≫ (natTransHσ q).app x✝¹ ≫ (alternatingFaceMapComplex C).map f =
    P q ≫ (alternatingFaceMapComplex C).map f + P q ≫ Hσ q ≫ (alternatingFaceMapComplex C).map f

Tactic:
]

Goal state after:
case succ
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X x✝¹ x✝ : SimplicialObject C
f : x✝¹ ⟶ x✝
q : ℕ
hq : (alternatingFaceMapComplex C).map f ≫ P q = P q ≫ (alternatingFaceMapComplex C).map f
⊢ P q ≫ (alternatingFaceMapComplex C).map f + P q ≫ (natTransHσ q).app x✝¹ ≫ (alternatingFaceMapComplex C).map f =
    P q ≫ (alternatingFaceMapComplex C).map f + P q ≫ Hσ q ≫ (alternatingFaceMapComplex C).map f
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 + z2‖ < ‖z1‖
hne : ¬‖z1‖ = ‖z2‖
⊢ ‖z1‖ ≤ max ‖z1‖ ‖z2‖

Tactic:
]

Goal state after:
p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 + z2‖ < ‖z1‖
hne : ¬‖z1‖ = ‖z2‖
⊢ ‖z1‖ ≤ max ‖z1‖ ‖z2‖
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 - z2‖ < ‖z2‖
⊢ ‖z1‖ = ‖-z2‖

Tactic:
]

Goal state after:
p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 - z2‖ < ‖z2‖
⊢ ‖z1‖ = ‖-z2‖
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ -φ ≫ X.δ ⟨a + 1, ⋯⟩ ≫ X.σ ⟨a, ⋯⟩ = -φ ≫ X.δ ⟨a + 1, ⋯⟩ ≫ X.σ ⟨a, ⋯⟩

pp: case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ Odd (a + (a + 1))

Tactic:
]

Goal state after:
case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ Odd (a + (a + 1))
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 - z2‖ < ‖z1‖
⊢ ‖z2‖ = ‖z1‖

Tactic:
]

Goal state after:
p : ℕ
hp : Fact (Nat.Prime p)
z1 z2 : ℚ_[p]
h : ‖z1 - z2‖ < ‖z1‖
⊢ ‖z2‖ = ‖z1‖
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ ((-1) ^ (a + 1) * (-1) ^ (a + 1)) • φ ≫ 𝟙 (X _⦋n + 1⦌) + ((-1) ^ (a + 2) * (-1) ^ (a + 1)) • φ ≫ 𝟙 (X _⦋n + 1⦌) = 0

Tactic:
]

Goal state after:
case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ ((-1) ^ (a + 1) * (-1) ^ (a + 1)) • φ ≫ 𝟙 (X _⦋n + 1⦌) + ((-1) ^ (a + 2) * (-1) ^ (a + 1)) • φ ≫ 𝟙 (X _⦋n + 1⦌) = 0
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
⊢ p.Coprime (p - 1)

Tactic:
]

Goal state after:
p : ℕ
hp : Fact (Nat.Prime p)
⊢ p.Coprime (p - 1)
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ ∑ x,
      (((-1) ^ ↑x * (-1) ^ (a + 1)) • φ ≫ X.σ ⟨a + 1, ⋯⟩ ≫ X.δ ⟨↑x, ⋯⟩ +
        ((-1) ^ a * (-1) ^ ↑x) • φ ≫ X.δ ⟨↑x, ⋯⟩ ≫ X.σ ⟨a, ⋯⟩) =
    0

Tactic:
]

Goal state after:
case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
⊢ ∑ x,
      (((-1) ^ ↑x * (-1) ^ (a + 1)) • φ ≫ X.σ ⟨a + 1, ⋯⟩ ≫ X.δ ⟨↑x, ⋯⟩ +
        ((-1) ^ a * (-1) ^ ↑x) • φ ≫ X.δ ⟨↑x, ⋯⟩ ≫ X.σ ⟨a, ⋯⟩) =
    0
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
i : ℕ
hi : i < a + 1
a✝ : ⟨i, hi⟩ ∈ Finset.univ
⊢ ↑⟨i, ⋯⟩ ≤ ↑⟨a, ⋯⟩.castSucc

Tactic:
]

Goal state after:
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
i : ℕ
hi : i < a + 1
a✝ : ⟨i, hi⟩ ∈ Finset.univ
⊢ ↑⟨i, ⋯⟩ ≤ ↑⟨a, ⋯⟩.castSucc
Module: Mathlib.AlgebraicTopology.DoldKan.Projections

Goal state before:
pp: C : Type u_1
inst✝⁴ : Category.{v_1, u_1} C
inst✝³ : Preadditive C
D : Type u_2
inst✝² : Category.{v_2, u_2} D
inst✝¹ : Preadditive D
G : C ⥤ D
inst✝ : G.Additive
X : SimplicialObject C
q n : ℕ
⊢ G.map (𝟙 (X _⦋n⦌)) = 𝟙 (((whiskering C D).obj G).obj X _⦋n⦌)

Tactic:
]

Goal state after:
C : Type u_1
inst✝⁴ : Category.{v_1, u_1} C
inst✝³ : Preadditive C
D : Type u_2
inst✝² : Category.{v_2, u_2} D
inst✝¹ : Preadditive D
G : C ⥤ D
inst✝ : G.Additive
X : SimplicialObject C
q n : ℕ
⊢ G.map (𝟙 (X _⦋n⦌)) = 𝟙 (((whiskering C D).obj G).obj X _⦋n⦌)
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
i : ℕ
hi : i < a + 1
a✝ : ⟨i, hi⟩ ∈ Finset.univ
hia : ⟨i, ⋯⟩ ≤ ⟨a, ⋯⟩.castSucc
pf✝⁴ : IsRightCancelAdd ℕ
pf✝³ : a + 1 < n + 1 + 1
pf✝² : i < n + 1 + 2
pf✝¹ : i < n + 2
pf✝ : a < n + 1
⊢ ((-1) ^ i * (-1) ^ (a + 1)) • φ ≫ X.δ ⟨i, ⋯⟩ ≫ X.σ ⟨a, ⋯⟩ = -((-1) ^ a * (-1) ^ i) • φ ≫ X.δ ⟨i, pf✝¹⟩ ≫ X.σ ⟨a, pf✝⟩

Tactic:
]

Goal state after:
case a
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n a q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hnaq : n = a + q
hnaq_shift : ∀ (d : ℕ), n + d = a + d + q
simplif : ∀ (a b c d e f : Y ⟶ X _⦋n + 1⦌), b = f → d + e = 0 → c + a = 0 → a + b + (c + d + e) = f
i : ℕ
hi : i < a + 1
a✝ : ⟨i, hi⟩ ∈ Finset.univ
hia : ⟨i, ⋯⟩ ≤ ⟨a, ⋯⟩.castSucc
pf✝⁴ : IsRightCancelAdd ℕ
pf✝³ : a + 1 < n + 1 + 1
pf✝² : i < n + 1 + 2
pf✝¹ : i < n + 2
pf✝ : a < n + 1
⊢ ((-1) ^ i * (-1) ^ (a + 1)) • φ ≫ X.δ ⟨i, ⋯⟩ ≫ X.σ ⟨a, ⋯⟩ = -((-1) ^ a * (-1) ^ i) • φ ≫ X.δ ⟨i, pf✝¹⟩ ≫ X.σ ⟨a, pf✝⟩
Module: Mathlib.AlgebraicTopology.DoldKan.PInfty

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
⊢ QInfty ≫ PInfty = 0

Tactic:
by
  ext n
  apply QInfty_f_comp_PInfty_f

Goal state after:
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
⊢ φ ≫ hσ' q (n + 1) (n + 2) ⋯ ≫ (AlternatingFaceMapComplex.obj X).d (n + 2) (n + 1) = 0

Tactic:
]

Goal state after:
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
⊢ φ ≫ hσ' q (n + 1) (n + 2) ⋯ ≫ (AlternatingFaceMapComplex.obj X).d (n + 2) (n + 1) = 0
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : n + 1 < q
⊢ 0 = 0

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case neg
p : ℕ
hp : Fact (Nat.Prime p)
f g : CauSeq ℚ (padicNorm p)
h : f ≈ g
hf : ¬f ≈ 0
hg : ¬g ≈ 0
⊢ PadicSeq.norm f = PadicSeq.norm g

Tactic:
]

Goal state after:
case neg
p : ℕ
hp : Fact (Nat.Prime p)
f g : CauSeq ℚ (padicNorm p)
h : f ≈ g
hf : ¬f ≈ 0
hg : ¬g ≈ 0
⊢ PadicSeq.norm f = PadicSeq.norm g
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case h
p : ℕ
hp : Fact (Nat.Prime p)
f : CauSeq ℚ (padicNorm p)
hf : ⟦f⟧ ≠ 0
⊢ ↑(↑p ^ (-PadicSeq.valuation f)) = ↑p ^ (-PadicSeq.valuation f)

pp: case h
p : ℕ
hp : Fact (Nat.Prime p)
f : CauSeq ℚ (padicNorm p)
hf : ⟦f⟧ ≠ 0
⊢ ¬f ≈ 0

Tactic:
]

Goal state after:
case h
p : ℕ
hp : Fact (Nat.Prime p)
f : CauSeq ℚ (padicNorm p)
hf : ⟦f⟧ ≠ 0
⊢ ↑(↑p ^ (-PadicSeq.valuation f)) = ↑p ^ (-PadicSeq.valuation f)

case h
p : ℕ
hp : Fact (Nat.Prime p)
f : CauSeq ℚ (padicNorm p)
hf : ⟦f⟧ ≠ 0
⊢ ¬f ≈ 0
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case h
p : ℕ
hp : Fact (Nat.Prime p)
f : CauSeq ℚ (padicNorm p)
hf : ⟦f⟧ ≠ 0
⊢ ↑p ^ (-PadicSeq.valuation f) = ↑p ^ (-PadicSeq.valuation f)

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case inr
p : ℕ
hp : Fact (Nat.Prime p)
q : ℚ
hq : q ≠ 0
⊢ padicNorm p q = ↑p ^ (-padicValRat p q)

Tactic:
]

Goal state after:
case inr
p : ℕ
hp : Fact (Nat.Prime p)
q : ℚ
hq : q ≠ 0
⊢ padicNorm p q = ↑p ^ (-padicValRat p q)
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
⊢ φ ≫ X.σ 0 ≫ ((-1) ^ ↑0 • X.δ 0) + φ ≫ X.σ 0 ≫ ((-1) ^ ↑(Fin.succ 0) • X.δ (Fin.succ 0)) = 0

pp: case neg.h
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
⊢ ∀ (a : Fin (n + 1)), φ ≫ X.σ 0 ≫ ((-1) ^ ↑a.succ.succ • X.δ a.succ.succ) = 0

Tactic:
]

Goal state after:
case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
⊢ φ ≫ X.σ 0 ≫ ((-1) ^ ↑0 • X.δ 0) + φ ≫ X.σ 0 ≫ ((-1) ^ ↑(Fin.succ 0) • X.δ (Fin.succ 0)) = 0

case neg.h
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
⊢ ∀ (a : Fin (n + 1)), φ ≫ X.σ 0 ≫ ((-1) ^ ↑a.succ.succ • X.δ a.succ.succ) = 0
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
n : ℤ
⊢ ↑(padicValInt p n) = ↑(padicValInt p n)

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
n : ℕ
⊢ ↑(padicValNat p n) = ↑(padicValNat p n)

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
⊢ 0 = 0

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
⊢ 1 = 1

Tactic:
]

Goal state after:
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case neg.h
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ 0 = 0

pp: case neg.h.hj₁
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ j.succ.succ.pred ⋯ ≠ 0

pp: case neg.h.hj₂
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ n + 2 ≤ ↑(j.succ.succ.pred ⋯) + q

pp: case neg.h.H
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ Fin.succ 0 < j.succ.succ

Tactic:
]

Goal state after:
case neg.h.hj₁
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ j.succ.succ.pred ⋯ ≠ 0

case neg.h.hj₂
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ n + 2 ≤ ↑(j.succ.succ.pred ⋯) + q

case neg.h.H
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
hqn : n < q
hqn' : ¬n + 1 < q
j : Fin (n + 1)
⊢ Fin.succ 0 < j.succ.succ
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hx : x ≠ 0
hy : y ≠ 0
h_norm : (x * y).valuation = x.valuation + y.valuation
hp_ne_one : ↑p ≠ 1
hp_pos : 0 < ↑p
⊢ (x * y).valuation = x.valuation + y.valuation

Tactic:
]

Goal state after:
p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hx : x ≠ 0
hy : y ≠ 0
h_norm : (x * y).valuation = x.valuation + y.valuation
hp_ne_one : ↑p ≠ 1
hp_pos : 0 < ↑p
⊢ (x * y).valuation = x.valuation + y.valuation
Module: Mathlib.AlgebraicTopology.DoldKan.PInfty

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
Y : Karoubi (SimplicialObject C)
n : ℕ
Y₁ : SimplexCategoryᵒᵖ ⥤ Karoubi C := (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj Y
Y₂ : SimplicialObject C := Y.X
Y₃ : SimplicialObject (Karoubi C) := ((whiskering C (Karoubi C)).obj (toKaroubi C)).obj Y.X
Y₄ : SimplexCategoryᵒᵖ ⥤ Karoubi C :=
  (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj ((toKaroubi (SimplexCategoryᵒᵖ ⥤ C)).obj Y.X)
P₁ : K[Y₁] ⟶ K[Y₁] := PInfty
P₂ : K[Y₂] ⟶ K[Y₂] := PInfty
P₃ : K[Y₃] ⟶ K[Y₃] := PInfty
P₄ : K[Y₄] ⟶ K[Y₄] := PInfty
h₃₂ : (P₃.f n).f = P₂.f n
h₄₃ : P₄.f n = P₃.f n
h₁₄ :
  PInfty.f n =
    (KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
      PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)
⊢ (P₁.f n).f = Y.p.app (op ⦋n⦌) ≫ P₂.f n

Tactic:
]

Goal state after:
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
Y : Karoubi (SimplicialObject C)
n : ℕ
Y₁ : SimplexCategoryᵒᵖ ⥤ Karoubi C := (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj Y
Y₂ : SimplicialObject C := Y.X
Y₃ : SimplicialObject (Karoubi C) := ((whiskering C (Karoubi C)).obj (toKaroubi C)).obj Y.X
Y₄ : SimplexCategoryᵒᵖ ⥤ Karoubi C :=
  (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj ((toKaroubi (SimplexCategoryᵒᵖ ⥤ C)).obj Y.X)
P₁ : K[Y₁] ⟶ K[Y₁] := PInfty
P₂ : K[Y₂] ⟶ K[Y₂] := PInfty
P₃ : K[Y₃] ⟶ K[Y₃] := PInfty
P₄ : K[Y₄] ⟶ K[Y₄] := PInfty
h₃₂ : (P₃.f n).f = P₂.f n
h₄₃ : P₄.f n = P₃.f n
h₁₄ :
  PInfty.f n =
    (KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
      PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)
⊢ (P₁.f n).f = Y.p.app (op ⦋n⦌) ≫ P₂.f n
Module: Mathlib.AlgebraicTopology.DoldKan.Decomposition

Goal state before:
pp: case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n q : ℕ
hq : (Q q).f (n + 1) = ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev
hqn : n < q
⊢ ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev =
    ∑ i with ↑i < q + 1, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev

Tactic:
]

Goal state after:
case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n q : ℕ
hq : (Q q).f (n + 1) = ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev
hqn : n < q
⊢ ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev =
    ∑ i with ↑i < q + 1, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case inr
p : ℕ
hp : Fact (Nat.Prime p)
x : ℚ_[p]
hx : x ≠ 0
h_norm : x⁻¹.valuation = -x.valuation
hp_ne_one : ↑p ≠ 1
hp_pos : 0 < ↑p
⊢ x⁻¹.valuation = -x.valuation

Tactic:
]

Goal state after:
case inr
p : ℕ
hp : Fact (Nat.Prime p)
x : ℚ_[p]
hx : x ≠ 0
h_norm : x⁻¹.valuation = -x.valuation
hp_ne_one : ↑p ≠ 1
hp_pos : 0 < ↑p
⊢ x⁻¹.valuation = -x.valuation
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: p : ℕ
hp : Fact (Nat.Prime p)
⊢ ⊤ = ⊤

Tactic:
]

Goal state after:
Module: Mathlib.AlgebraicTopology.DoldKan.Decomposition

Goal state before:
pp: case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n q : ℕ
hq : (Q q).f (n + 1) = ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev
hqn : q ≤ n
a : ℕ
ha : q + a = n
⊢ ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev - (P q).f (n + 1) ≫ (Hσ q).f (n + 1) =
    ∑ i with ↑i < q + 1, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev

Tactic:
]

Goal state after:
case neg
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
n q : ℕ
hq : (Q q).f (n + 1) = ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev
hqn : q ≤ n
a : ℕ
ha : q + a = n
⊢ ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev - (P q).f (n + 1) ≫ (Hσ q).f (n + 1) =
    ∑ i with ↑i < q + 1, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case pos
p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hx : x = 0
⊢ ⊤ = ⊤

Tactic:
]

Goal state after:
Module: Mathlib.AlgebraicTopology.DoldKan.PInfty

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
Y : Karoubi (SimplicialObject C)
n : ℕ
Y₁ : SimplexCategoryᵒᵖ ⥤ Karoubi C := (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj Y
Y₂ : SimplicialObject C := Y.X
Y₃ : SimplicialObject (Karoubi C) := ((whiskering C (Karoubi C)).obj (toKaroubi C)).obj Y.X
Y₄ : SimplexCategoryᵒᵖ ⥤ Karoubi C :=
  (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj ((toKaroubi (SimplexCategoryᵒᵖ ⥤ C)).obj Y.X)
P₁ : K[Y₁] ⟶ K[Y₁] := PInfty
P₂ : K[Y₂] ⟶ K[Y₂] := PInfty
P₃ : K[Y₃] ⟶ K[Y₃] := PInfty
P₄ : K[Y₄] ⟶ K[Y₄] := PInfty
h₃₂ : (P₃.f n).f = P₂.f n
h₄₃ : P₄.f n = P₃.f n
h₁₄ :
  PInfty.f n =
    (KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
      PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)
⊢ ((KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
        PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)).f =
    Y.p.app (op ⦋n⦌) ≫ (P₄.f n).f

Tactic:
]

Goal state after:
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
Y : Karoubi (SimplicialObject C)
n : ℕ
Y₁ : SimplexCategoryᵒᵖ ⥤ Karoubi C := (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj Y
Y₂ : SimplicialObject C := Y.X
Y₃ : SimplicialObject (Karoubi C) := ((whiskering C (Karoubi C)).obj (toKaroubi C)).obj Y.X
Y₄ : SimplexCategoryᵒᵖ ⥤ Karoubi C :=
  (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj ((toKaroubi (SimplexCategoryᵒᵖ ⥤ C)).obj Y.X)
P₁ : K[Y₁] ⟶ K[Y₁] := PInfty
P₂ : K[Y₂] ⟶ K[Y₂] := PInfty
P₃ : K[Y₃] ⟶ K[Y₃] := PInfty
P₄ : K[Y₄] ⟶ K[Y₄] := PInfty
h₃₂ : (P₃.f n).f = P₂.f n
h₄₃ : P₄.f n = P₃.f n
h₁₄ :
  PInfty.f n =
    (KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
      PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)
⊢ ((KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
        PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)).f =
    Y.p.app (op ⦋n⦌) ≫ (P₄.f n).f
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case pos
p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hx : ¬x = 0
hy : y = 0
⊢ ⊤ = ⊤

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case neg
p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hx : ¬x = 0
hy : ¬y = 0
⊢ x.valuation + y.valuation = x.valuation + y.valuation

Tactic:
]

Goal state after:
Module: Mathlib.AlgebraicTopology.DoldKan.Faces

Goal state before:
pp: case pos
C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
X : SimplicialObject C
Y : C
n q : ℕ
φ : Y ⟶ X _⦋n + 1⦌
v : HigherFacesVanish q φ
j : Fin (n + 1)
hj₁ : n + 1 ≤ ↑j + (q + 1)
hqn : n < q
⊢ 0 = 0

Tactic:
]

Goal state after:
Module: Mathlib.AlgebraicTopology.DoldKan.PInfty

Goal state before:
pp: C : Type u_1
inst✝¹ : Category.{v_1, u_1} C
inst✝ : Preadditive C
Y : Karoubi (SimplicialObject C)
n : ℕ
Y₁ : SimplexCategoryᵒᵖ ⥤ Karoubi C := (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj Y
Y₂ : SimplicialObject C := Y.X
Y₃ : SimplicialObject (Karoubi C) := ((whiskering C (Karoubi C)).obj (toKaroubi C)).obj Y.X
Y₄ : SimplexCategoryᵒᵖ ⥤ Karoubi C :=
  (karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).obj ((toKaroubi (SimplexCategoryᵒᵖ ⥤ C)).obj Y.X)
P₁ : K[Y₁] ⟶ K[Y₁] := PInfty
P₂ : K[Y₂] ⟶ K[Y₂] := PInfty
P₃ : K[Y₃] ⟶ K[Y₃] := PInfty
P₄ : K[Y₄] ⟶ K[Y₄] := PInfty
h₃₂ : (P₃.f n).f = P₂.f n
h₄₃ : P₄.f n = P₃.f n
h₁₄ :
  PInfty.f n =
    (KaroubiFunctorCategoryEmbedding.map Y.decompId_i).app (op ⦋n⦌) ≫
      PInfty.f n ≫ (KaroubiFunctorCategoryEmbedding.map Y.decompId_p).app (op ⦋n⦌)
π : Y₄ ⟶ Y₄ := (toKaroubi (SimplexCategoryᵒᵖ ⥤ C) ⋙ karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C).map Y.p
eq : Y.p.app (op ⦋n⦌) ≫ (PInfty.f n).f = (PInfty.f n).f ≫ Y.p.app (op ⦋n⦌)
⊢ Y.p.app (op ⦋n⦌) ≫ (PInfty.f n).f = Y.p.app (op ⦋n⦌) ≫ (P₄.f n).f

Tactic:
]

Goal state after:
Module: Mathlib.NumberTheory.Padics.PadicNumbers

Goal state before:
pp: case pos
p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hxy : x + y = 0
⊢ min (if x = 0 then ⊤ else ↑x.valuation) (if y = 0 then ⊤ else ↑y.valuation) ≤ ⊤

Tactic:
]

Goal state after:
case pos
p : ℕ
hp : Fact (Nat.Prime p)
x y : ℚ_[p]
hxy : x + y = 0
⊢ min (if x = 0 then ⊤ else ↑x.valuation) (if y = 0 then ⊤ else ↑y.valuation) ≤ ⊤