theorem extracted_formal_statement_17.{w, v, u} {Z : Type w} {ι : Type v} {f : ι → Z → ℝ} {Ω : Type u}
  [inst : MeasurableSpace Ω] {X : Ω → Z} {μ : Measure Ω} [inst_1 : IsProbabilityMeasure μ] [inst_2 : Countable ι]
  [inst_3 : Nonempty ι] (h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)) {b : ℝ} (h𝓕' : ∀ (I : ι) (z : Z), |f I z| ≤ b) {n : ℕ}
  {c : ι → ℝ} {C : ℝ} (hC : ∀ (I : ι), |c I| ≤ C) (σ : Fin n → { x // x ∈ {-1, 1} }) (a : σ ∈ Finset.univ) (I : ι) :
  Measurable fun b =>
    ∑ i, ↑↑(σ i) * (f I (X (b.2 i).1) - f I (X (b.2 i).2)) + (f I (X b.1.1) - f I (X b.1.2) + c I) := sorry

State before:
case left.hf.hf.hf.hf
Z : Type w
ι : Type v
f : ι → Z → ℝ
Ω : Type u
inst✝³ : MeasurableSpace Ω
X : Ω → Z
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
inst✝¹ : Countable ι
inst✝ : Nonempty ι
h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
b : ℝ
h𝓕' : ∀ (I : ι) (z : Z), |f I z| ≤ b
n : ℕ
c : ι → ℝ
C : ℝ
hC : ∀ (I : ι), |c I| ≤ C
σ : Fin n → { x // x ∈ {-1, 1} }
a✝ : σ ∈ Finset.univ
I : ι
⊢ Measurable fun b => ∑ i, ↑↑(σ i) * (f I (X (b.2 i).1) - f I (X (b.2 i).2)) + (f I (X b.1.1) - f I (X b.1.2) + c I)

Tactic: apply Measurable.add
    ·
  apply Finset.measurable_sum Finset.univ
  intro i _
  apply Measurable.const_mul
  exact (measurable_sub_part h𝓕).comp measurable_snd
    ·
  apply Measurable.add_const
  to_theorem
    apply
      Measurable.sub·
      exact (h𝓕 I).comp <| measurable_fst.comp measurable_fst· exact (h𝓕 I).comp <| measurable_snd.comp measurable_fst

State after:

Relevant lemmas:
error