theorem extracted_formal_statement_53.{w, v, u} {Z : Type w} {ι : Type v} {f : ι → Z → ℝ} {Ω : Type u}
  [inst : MeasurableSpace Ω] {X : Ω → Z} [inst_1 : Countable ι] (h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)) (n : ℕ)
  (c : ι → ℝ) (I : ι) (h_original_goal : Measurable fun b => ∑ i, (f I (X (b i).1) - f I (X (b i).2)) + c I) :
  Measurable fun x => ∑ i, (f I (X (x i).1) - f I (X (x i).2)) := sorry

State before:
case hf
Z : Type w
ι : Type v
f : ι → Z → ℝ
Ω : Type u
inst✝¹ : MeasurableSpace Ω
X : Ω → Z
inst✝ : Countable ι
h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
n : ℕ
c : ι → ℝ
I : ι
⊢ Measurable fun b => ∑ i, (f I (X (b i).1) - f I (X (b i).2)) + c I

Tactic: apply Measurable.add_const

State after:
[case hf.hf
 Z : Type w
 ι : Type v
 f : ι → Z → ℝ
 Ω : Type u
 inst✝¹ : MeasurableSpace Ω
 X : Ω → Z
 inst✝ : Countable ι
 h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
 n : ℕ
 c : ι → ℝ
 I : ι
 ⊢ Measurable fun x => ∑ i, (f I (X (x i).1) - f I (X (x i).2))]

Relevant lemmas:
Measurable.add_const : ∀ {M : Type u_2} {α : Type u_3} [inst : MeasurableSpace M] [inst_2 : Add M]
  {m : MeasurableSpace α} {f : α → M} [inst_3 : MeasurableAdd M], Measurable f → ∀ (c : M), Measurable fun x => f x + c