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 j : ℕ
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) ⋯).X 0)
      (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 0) :
        C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).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) ⋯).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) ⋯).X 0)
⊢ (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 succ : ∀ (j : ℕ),
  (ComplexShape.down ℕ).Rel 1 (j + 1) →
    Eq.{v + 1} (α := C.X 1 ⟶ ((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 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 (j + 1)) :
        C.X 1 ⟶ ((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 1 (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 1 ⟶ ((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 1 0 →
    Eq.{v + 1} (α := C.X 1 ⟶ ((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 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 0) :
        C.X 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).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) ⋯).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) ⋯).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 := C.X 1 ⟶ ((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 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 + 1)) :
        C.X 1 ⟶ ((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 1 (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 1 ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).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 := C.X (n + 2) ⟶ ((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 (n + 2))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x)
            n + 2 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 (n + 2) j) :
        C.X (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (C.d (n + 2) 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 (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
have zero : (ComplexShape.down ℕ).Rel (n + 2) 0 →
  Eq.{v + 1} (α := C.X (n + 2) ⟶ ((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 (n + 2))
        (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) n + 2 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 (n + 2) 0) :
      C.X (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X 0)
    (CategoryStruct.comp (Y := C.X 0) (C.d (n + 2) 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 (n + 2) ⟶ ((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 : ℕ
zero :
  (ComplexShape.down ℕ).Rel (n + 2) 0 →
    Eq.{v + 1} (α := C.X (n + 2) ⟶ ((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 (n + 2))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x)
            n + 2 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 (n + 2) 0) :
        C.X (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
      (CategoryStruct.comp (Y := C.X 0) (C.d (n + 2) 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 (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
⊢ (ComplexShape.down ℕ).Rel (n + 2) j →
    Eq.{v + 1} (α := C.X (n + 2) ⟶ ((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 (n + 2))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x)
            n + 2 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 (n + 2) j) :
        C.X (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
      (C.d (n + 2) 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 (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X j)
have succ : ∀ (j : ℕ),
  (ComplexShape.down ℕ).Rel (n + 2) (j + 1) →
    Eq.{v + 1} (α := C.X (n + 2) ⟶ ((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 (n + 2))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x)
            n + 2 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 (n + 2) (j + 1)) :
        C.X (n + 2) ⟶ ((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 (n + 2) (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 (n + 2) ⟶ ((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 : ℕ
⊢ (ComplexShape.down ℕ).Rel (n + 2) 0 →
    Eq.{v + 1} (α := C.X (n + 2) ⟶ ((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 (n + 2))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x)
            n + 2 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 (n + 2) 0) :
        C.X (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
      (CategoryStruct.comp (Y := C.X 0) (C.d (n + 2) 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 (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X 0)
have zero : 1 = n + 2 →
  (𝟙 (C.X (n + 1 + 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, 0 with
      | 1, 0 => C.d 1 0
      | i.succ, j.succ => C.d (i + 1) (j + 1)
      | x, x_1 => 0) =
    C.d (n + 2) 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 := C.X (n + 2) ⟶ ((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 (n + 2))
          (match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x)
            n + 2 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 (n + 2) (j + 1)) :
        C.X (n + 2) ⟶ ((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 (n + 2) (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 (n + 2) ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X (j + 1))
have succ : j + 1 + 1 = n + 2 →
  (𝟙 (C.X (n + 1 + 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) =
    C.d (n + 2) (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
⊢ CategoryStruct.comp (Y := C)
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) x 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)),
        comm' := ⋯ }
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) x with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)),
        comm' := ⋯ } =
    𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯)
have h : ∀ (i : ℕ),
  Hom.f
      (CategoryStruct.comp (Y := C)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) x 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)),
          comm' := sorry }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := sorry })
      i =
    Hom.f (𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry)) i
Tactic: ext i
-- 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
⊢ Hom.f
      (CategoryStruct.comp (Y := C)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) x 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)),
          comm' := ⋯ }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := ⋯ })
      i =
    Hom.f (𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯)) i
have h : Eq (α :=
  ((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).X 0)
  (Hom.f
    (CategoryStruct.comp (Y := C)
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) x 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)),
        comm' := sorry }
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) x with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)),
        comm' := sorry })
    0)
  (Hom.f (𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry)) 0)
Tactic: cases i
Cleared hypotheses: i
-- 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
h :
  Eq (α :=
    ((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) ⋯).X 0)
    (Hom.f
      (CategoryStruct.comp (Y := C)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) x 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)),
          comm' := ⋯ }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := ⋯ })
      0)
    (Hom.f (𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯)) 0)
⊢ Hom.f
      (CategoryStruct.comp (Y := C)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) x 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)),
          comm' := ⋯ }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := ⋯ })
      i =
    Hom.f (𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯)) i
have h₁ : ∀ (n : ℕ),
  Hom.f
      (CategoryStruct.comp (Y := C)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) x 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)),
          comm' := sorry }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := sorry })
      (n + 1) =
    Hom.f (𝟙 ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry)) (n + 1)
Tactic: cases i
Cleared hypotheses: i
-- 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
⊢ CategoryStruct.comp (Y := (Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯)
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) x with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)),
        comm' := ⋯ }
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) x 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)),
        comm' := ⋯ } =
    𝟙 C
have h : ∀ (i : ℕ),
  Hom.f
      (CategoryStruct.comp (Y := (Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := sorry }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) x 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)),
          comm' := sorry })
      i =
    Hom.f (𝟙 C) i
Tactic: ext i
-- 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
⊢ Hom.f
      (CategoryStruct.comp (Y := (Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯)
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x) x with
            | 0 => 𝟙 (C.X 0)
            | n.succ => 𝟙 (C.X (n + 1)),
          comm' := ⋯ }
        {
          f := fun (x : ℕ) ↦
            match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) ⋯).X x ⟶ C.X x) x 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)),
          comm' := ⋯ })
      i =
    Hom.f (𝟙 C) i
have h : Eq (α := C.X 0 ⟶ C.X 0)
  (Hom.f
    (CategoryStruct.comp (Y := (Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry)
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → C.X x ⟶ ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x) x with
          | 0 => 𝟙 (C.X 0)
          | n.succ => 𝟙 (C.X (n + 1)),
        comm' := sorry }
      {
        f := fun (x : ℕ) ↦
          match (motive := (x : ℕ) → ((Functor.obj truncate C).augment (X := C.X 0) (C.d 1 0) sorry).X x ⟶ C.X x) x 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)),
        comm' := sorry })
    0)
  (Hom.f (𝟙 C) 0)
Tactic: cases i
Cleared hypotheses: i