theorem extracted_formal_statement_0.{u_2, u_1} {Ω : Type u_1} [inst : MeasurableSpace Ω] {μ : Measure Ω}
  [inst_1 : IsProbabilityMeasure μ] {E : Type u_2} [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace ℝ E]
  {f : Ω → E} {C : ℝ} (h : ∀ᵐ (x : Ω) ∂μ, ‖f x‖ ≤ C) : ‖∫ (x : Ω), f x ∂μ‖ ≤ C * (μ Set.univ).toReal := sorry

State before:
Ω : Type u_1
inst✝³ : MeasurableSpace Ω
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
f : Ω → E
C : ℝ
h : ∀ᵐ (x : Ω) ∂μ, ‖f x‖ ≤ C
⊢ ‖∫ (x : Ω), f x ∂μ‖ ≤ C * (μ Set.univ).toReal

Tactic: apply norm_integral_le_of_norm_le_const h

State after:

Relevant lemmas:
MeasureTheory.norm_integral_le_of_norm_le_const : ∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G]
  [inst_4 : NormedSpace ℝ G] {m : MeasurableSpace α} {μ : Measure α} [inst_5 : IsFiniteMeasure μ] {f : α → G} {C : ℝ},
  (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ C) → ‖∫ (x : α), f x ∂μ‖ ≤ C * (μ Set.univ).toReal