theorem extracted_formal_statement_1.{u} {Ω : Type u} [inst : MeasurableSpace Ω] (μ : Measure Ω := by volume_tac)
  [inst_1 : IsProbabilityMeasure μ] {X : Ω → ℝ} (h0 : ∫ (x : Ω), X x ∂μ = 0) : ∫ (x : Ω), X x ∂μ = 0 := sorry

State before:
Ω : Type u
inst✝¹ : MeasurableSpace Ω
μ : autoParam (Measure Ω) _auto✝
inst✝ : IsProbabilityMeasure μ
X : Ω → ℝ
h0 : ∫ (x : Ω), X x ∂μ = 0
⊢ ∫ (x : Ω), X x ∂μ = 0

Tactic: exact h0

State after:

Relevant lemmas: