theorem extracted_formal_statement_283.{u_3, u_2, u_1} {Ω : Type u_1} [inst : MeasurableSpace Ω] {μ : Measure Ω}
  [inst_1 : IsProbabilityMeasure μ] {𝓧 : Type u_2} {ι : Type u_3} [inst_2 : DecidableEq ι] {m𝓧 : MeasurableSpace 𝓧}
  [hnonempty𝓧 : Nonempty 𝓧] [inst_3 : Fintype ι] (X : ι → Ω → 𝓧) (hX : ∀ (i : ι), Measurable (X i))
  (hX' : iIndepFun X μ) (f : (ι → 𝓧) → ℝ) (c : ι → ℝ)
  (hf : ∀ (i : ι) (x : ι → 𝓧) (x' : 𝓧), |f x - f (Function.update x i x')| ≤ c i) (hf' : Measurable f) (t : ℝ)
  (ht' : t * ∑ i, c i ^ 2 ≤ 1) (hmf : ∀ (i : ι) (x : ι → 𝓧) (x' : 𝓧), |(-f) x - (-f) (Function.update x i x')| ≤ c i) :
  Measurable (-f) := sorry

State before:
Ω : Type u_1
inst✝³ : MeasurableSpace Ω
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
𝓧 : Type u_2
ι : Type u_3
inst✝¹ : DecidableEq ι
m𝓧 : MeasurableSpace 𝓧
hnonempty𝓧 : Nonempty 𝓧
inst✝ : Fintype ι
X : ι → Ω → 𝓧
hX : ∀ (i : ι), Measurable (X i)
hX' : iIndepFun X μ
f : (ι → 𝓧) → ℝ
c : ι → ℝ
hf : ∀ (i : ι) (x : ι → 𝓧) (x' : 𝓧), |f x - f (Function.update x i x')| ≤ c i
hf' : Measurable f
ε : ℝ
hε : ε > 0
t : ℝ
ht' : t * ∑ i, c i ^ 2 ≤ 1
hmf : ∀ (i : ι) (x : ι → 𝓧) (x' : 𝓧), |(-f) x - (-f) (Function.update x i x')| ≤ c i
⊢ Measurable (-f)

Tactic: apply Measurable.comp measurable_neg hf'

State after:

Relevant lemmas:
Measurable.comp : ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {x : MeasurableSpace α} {x_1 : MeasurableSpace β}
  {x_2 : MeasurableSpace γ} {g : β → γ} {f : α → β}, Measurable g → Measurable f → Measurable (g ∘ f)
MeasurableNeg.measurable_neg : ∀ {G : Type u_2} {inst : Neg G} {inst_4 : MeasurableSpace G} [self : MeasurableNeg G],
  Measurable Neg.neg