case h
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
j : Fin (n + 1)
hj₁ : n + 1 ≤ ↑j + 0
⊢ False
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
j : Fin (n + 1)
hj₁ : n + 1 ≤ ↑j + 0
⊢ HomologicalComplex.Hom.f (P 0) (n + 1) ≫ δ X (Fin.succ j) = 0
exfalso
case h
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
j : Fin (n + 1)
hj₁ : n + 1 ≤ ↑j + 0
hj₂ : ↑j < n + 1
⊢ False
case h
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
j : Fin (n + 1)
hj₁ : n + 1 ≤ ↑j + 0
⊢ False
have hj₂ := Fin.is_lt j
no goals
case h
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
n : ℕ
j : Fin (n + 1)
hj₁ : n + 1 ≤ ↑j + 0
hj₂ : ↑j < n + 1
⊢ False
linarith
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
q n : ℕ
⊢ HigherFacesVanish (q + 1) (HomologicalComplex.Hom.f (P q ≫ (𝟙 K[X] + Hσ q)) (n + 1))
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
q n : ℕ
⊢ HigherFacesVanish (q + 1) (HomologicalComplex.Hom.f (P (q + 1)) (n + 1))
simp only [P_succ]
no goals
C : Type u_1
inst✝¹ : Category C
inst✝ : Preadditive C
X : SimplicialObject C
q n : ℕ
⊢ HigherFacesVanish (q + 1) (HomologicalComplex.Hom.f (P q ≫ (𝟙 K[X] + Hσ q)) (n + 1))
exact (of_P q n).induction