Module: Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj

Goal state before:
pp: case pos
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : i ≤ a
h3 : i = a + 1
⊢ x₀ i = ⋯ ▸ x

pp: case neg
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : i ≤ a
h3 : ¬i = a + 1
⊢ x₀ i = x₀ i

pp: case pos
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : ¬i ≤ a
h✝ : i = a + 1
⊢ { toFun := fun x i ↦ ⋯ ▸ x, invFun := fun x ↦ x ⟨a + 1, ⋯⟩, left_inv := ⋯, right_inv := ⋯ } x ⟨i, ⋯⟩ = ⋯ ▸ x

pp: case neg
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : ¬i ≤ a
h✝ : ¬i = a + 1
⊢ { toFun := fun x i ↦ ⋯ ▸ x, invFun := fun x ↦ x ⟨a + 1, ⋯⟩, left_inv := ⋯, right_inv := ⋯ } x ⟨i, ⋯⟩ = x₀ i

pp: case pos
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : ¬i ≤ a + 1
h✝ : i = a + 1
⊢ x₀ i = ⋯ ▸ x

pp: case neg
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : ¬i ≤ a + 1
h✝ : ¬i = a + 1
⊢ x₀ i = x₀ i

Tactic:
<;>

Goal state after:
case pos
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : i ≤ a
h3 : i = a + 1
⊢ x₀ i = ⋯ ▸ x

case neg
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : i ≤ a
h3 : ¬i = a + 1
⊢ x₀ i = x₀ i

case pos
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : ¬i ≤ a
h✝ : i = a + 1
⊢ { toFun := fun x i ↦ ⋯ ▸ x, invFun := fun x ↦ x ⟨a + 1, ⋯⟩, left_inv := ⋯, right_inv := ⋯ } x ⟨i, ⋯⟩ = ⋯ ▸ x

case neg
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : i ≤ a + 1
h2 : ¬i ≤ a
h✝ : ¬i = a + 1
⊢ { toFun := fun x i ↦ ⋯ ▸ x, invFun := fun x ↦ x ⟨a + 1, ⋯⟩, left_inv := ⋯, right_inv := ⋯ } x ⟨i, ⋯⟩ = x₀ i

case pos
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : ¬i ≤ a + 1
h✝ : i = a + 1
⊢ x₀ i = ⋯ ▸ x

case neg
X : ℕ → Type u_1
mX : (n : ℕ) → MeasurableSpace (X n)
κ : (n : ℕ) → Kernel ((i : ↥(Iic n)) → X ↑i) (X (n + 1))
inst✝ : ∀ (n : ℕ), IsSFiniteKernel (κ n)
a : ℕ
f : ((n : ℕ) → X n) → ℝ≥0∞
mf : Measurable f
x₀ : (n : ℕ) → X n
x : X (a + 1)
i : ℕ
h1 : ¬i ≤ a + 1
h✝ : ¬i = a + 1
⊢ x₀ i = x₀ i