awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i : ℕ
⊢ (ComplexShape.down ℕ).Rel 0 0 →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0 ⟶ C.X 0)
      (CategoryStruct.comp (Y := C.X 0)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 0 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d 0 0) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0 ⟶ C.X 0)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 0)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 0 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1))) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0 ⟶ C.X 0)
have zero : Eq (α := ℕ) 1 0 → 𝟙 (C.X 0) ≫ C.d 0 0 = 0 ≫ 𝟙 (C.X 0)
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
⊢ (ComplexShape.down ℕ).Rel 0 (j + 1) →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0 ⟶ C.X (j + 1))
      (CategoryStruct.comp (Y := C.X 0)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 0 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d 0 (j + 1)) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0 ⟶ C.X (j + 1))
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 (j + 1))
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x)
            j + 1 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1))) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0 ⟶ C.X (j + 1))
have succ : j + 1 + 1 = 0 → 𝟙 (C.X 0) ≫ C.d 0 (j + 1) = 0 ≫ 𝟙 (C.X (j + 1))
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
⊢ (ComplexShape.down ℕ).Rel 1 j →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X j)
      (CategoryStruct.comp (Y := C.X 1)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 1 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d 1 j) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X j)
      (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 1 j ≫
          match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) j with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X j)
have zero : (ComplexShape.down ℕ).Rel 1 0 →
  Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 1 ⟶ C.X 0)
    (CategoryStruct.comp (Y := C.X 1)
        (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) 1 with
        | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 1)))
        (C.d 1 0) :
      ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 1 ⟶ C.X 0)
    (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).d 1 0)
        (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) 0 with
        | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 1))) :
      ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 1 ⟶ C.X 0)
Tactic: rcases j with - | j
Cleared hypotheses: j
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i : ℕ
⊢ (ComplexShape.down ℕ).Rel 1 0 →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X 0)
      (CategoryStruct.comp (Y := C.X 1)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 1 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d 1 0) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X 0)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 1 0)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 0 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1))) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X 0)
have zero : Eq (α := ℕ) 1 1 → 𝟙 (C.X 1) ≫ C.d 1 0 = C.d 1 0 ≫ 𝟙 (C.X 0)
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
⊢ (ComplexShape.down ℕ).Rel 1 (j + 1) →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X (j + 1))
      (CategoryStruct.comp (Y := C.X 1)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 1 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d 1 (j + 1)) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X (j + 1))
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 1 (j + 1))
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x)
            j + 1 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1))) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1 ⟶ C.X (j + 1))
have succ : j + 1 + 1 = 1 → 𝟙 (C.X 1) ≫ C.d 1 (j + 1) = C.d 1 (j + 1) ≫ 𝟙 (C.X (j + 1))
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j n : ℕ
⊢ (ComplexShape.down ℕ).Rel (n + 2) j →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X j)
      (CategoryStruct.comp (Y := C.X (n + 2))
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x)
            n + 2 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d (n + 2) j) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X j)
      (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d (n + 2) j ≫
          match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) j with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X j)
have zero : (ComplexShape.down ℕ).Rel (n + 2) 0 →
  Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 2) ⟶ C.X 0)
    (CategoryStruct.comp (Y := C.X (n + 2))
        (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) n + 2 with
        | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 1)))
        (C.d (n + 2) 0) :
      ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 2) ⟶ C.X 0)
    (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).d (n + 2) 0)
        (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) 0 with
        | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 1))) :
      ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (n + 2) ⟶ C.X 0)
Tactic: rcases j with - | j
Cleared hypotheses: j
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i n : ℕ
⊢ (ComplexShape.down ℕ).Rel (n + 2) 0 →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X 0)
      (CategoryStruct.comp (Y := C.X (n + 2))
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x)
            n + 2 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d (n + 2) 0) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X 0)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d (n + 2) 0)
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) 0 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1))) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X 0)
have zero : 1 = n + 2 →
  Eq (α := C.X (n + 1 + 1) ⟶ C.X 0) (𝟙 (C.X (n + 1 + 1)) ≫ C.d (n + 2) 0)
    ((match (motive :=
        (x x_1 : ℕ) →
          Quiver.Hom.{v, u} (V := V)
            (match (motive := ℕ → V) x with
              | 0 => C.X 0
              | i.succ => C.X (i + 1) :
              V)
            (match (motive := ℕ → V) x_1 with
              | 0 => C.X 0
              | i.succ => C.X (i + 1) :
              V))
        n + 2, 0 with
      | 1, 0 => C.d 1 0
      | i.succ, j.succ => C.d (i + 1) (j + 1)
      | x, x_1 => 0) ≫
      𝟙 (C.X 0))
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i n j : ℕ
⊢ (ComplexShape.down ℕ).Rel (n + 2) (j + 1) →
    Eq.{v + 1} (α := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X (j + 1))
      (CategoryStruct.comp (Y := C.X (n + 2))
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x)
            n + 2 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1)))
          (C.d (n + 2) (j + 1)) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X (j + 1))
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d (n + 2) (j + 1))
          (match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x)
            j + 1 with
          | 0 => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          | n.succ => 𝟙 (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 1))) :
        ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (n + 2) ⟶ C.X (j + 1))
have succ : j + 1 + 1 = n + 2 →
  Eq (α := C.X (n + 1 + 1) ⟶ C.X (j + 1)) (𝟙 (C.X (n + 1 + 1)) ≫ C.d (n + 2) (j + 1))
    ((match (motive :=
        (x x_1 : ℕ) →
          Quiver.Hom.{v, u} (V := V)
            (match (motive := ℕ → V) x with
              | 0 => C.X 0
              | i.succ => C.X (i + 1) :
              V)
            (match (motive := ℕ → V) x_1 with
              | 0 => C.X 0
              | i.succ => C.X (i + 1) :
              V))
        n + 2, j + 1 with
      | 1, 0 => C.d 1 0
      | i.succ, j.succ => C.d (i + 1) (j + 1)
      | x, x_1 => 0) ≫
      𝟙 (C.X (j + 1)))
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
⊢ (ComplexShape.down ℕ).Rel 0 j →
    Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 j) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (C.d 0 j ≫
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) j with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
have zero : (ComplexShape.down ℕ).Rel 0 0 →
  Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
    (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
        (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) 0 with
        | 0 => 𝟙 (C.X 0)
        | n.succ => 𝟙 (C.X (n + 1)))
        (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).d 0 0) :
      C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
    (CategoryStruct.comp (Y := C.X 0) (C.d 0 0)
        (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) 0 with
        | 0 => 𝟙 (C.X 0)
        | n.succ => 𝟙 (C.X (n + 1))) :
      C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
Tactic: rcases j with - | j
Cleared hypotheses: j
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
zero :
  (ComplexShape.down ℕ).Rel 0 0 →
    Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 0) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
      (CategoryStruct.comp (Y := C.X 0) (C.d 0 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1))) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
⊢ (ComplexShape.down ℕ).Rel 0 j →
    Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 j) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (C.d 0 j ≫
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) j with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
have succ : ∀ (j : ℕ),
  (ComplexShape.down ℕ).Rel 0 (j + 1) →
    Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (j + 1))
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).d 0 (j + 1)) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (j + 1))
      (CategoryStruct.comp (Y := C.X (j + 1)) (C.d 0 (j + 1))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x)
            j + 1 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1))) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X (j + 1))
Tactic: rcases j with - | j
Cleared hypotheses: j
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i : ℕ
⊢ (ComplexShape.down ℕ).Rel 0 0 →
    Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 0) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
      (CategoryStruct.comp (Y := C.X 0) (C.d 0 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1))) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
have zero : Eq (α := ℕ) 1 0 → 𝟙 (C.X 0) ≫ 0 = C.d 0 0 ≫ 𝟙 (C.X 0)
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
⊢ (ComplexShape.down ℕ).Rel 0 (j + 1) →
    Eq.{v + 1} (α := C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 0 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 0 (j + 1)) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
      (CategoryStruct.comp (Y := C.X (j + 1)) (C.d 0 (j + 1))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x)
            j + 1 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1))) :
        C.X 0 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
have succ : j + 1 + 1 = 0 → 𝟙 (C.X 0) ≫ 0 = C.d 0 (j + 1) ≫ 𝟙 (C.X (j + 1))
Tactic: dsimp [augment, truncate]
-- Lean 4 proof step from Mathlib.Algebra.Homology.Augment (goal)
Goal:
V : Type u
inst : Category.{v, u} V
inst_1 : HasZeroMorphisms.{v, u} V
C : ChainComplex.{v, u, 0} V ℕ
i j : ℕ
⊢ (ComplexShape.down ℕ).Rel 1 j →
    Eq.{v + 1} (α := C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 1)
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) 1 with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)))
          (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).d 1 j) :
        C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (C.d 1 j ≫
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) j with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)) :
        C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
have zero : (ComplexShape.down ℕ).Rel 1 0 →
  Eq.{v + 1} (α := C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
    (CategoryStruct.comp (Y := ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 1)
        (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) 1 with
        | 0 => 𝟙 (C.X 0)
        | n.succ => 𝟙 (C.X (n + 1)))
        (((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).d 1 0) :
      C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
    (CategoryStruct.comp (Y := C.X 0) (C.d 1 0)
        (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) 0 with
        | 0 => 𝟙 (C.X 0)
        | n.succ => 𝟙 (C.X (n + 1))) :
      C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
Tactic: rcases j with - | j
Cleared hypotheses: j