zzhisthebest/LeanBenchmark huggingface dataset:
import Mathlib
import FoML


open MeasureTheory ProbabilityTheory

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

Tactic 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

Tactic state after:
import Mathlib
import FoML


open MeasureTheory ProbabilityTheory

theorem extracted_formal_statement_1.{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] {f : Ω → E} {C : ℝ}
  (h : ∀ᵐ (x : Ω) ∂μ, ‖f x‖ ≤ C) (this : μ Set.univ = 1) (h_original_goal : C * (μ Set.univ).toReal = C) :
  C * ENNReal.toReal 1 = C := sorry

Tactic 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
this : μ Set.univ = 1
⊢ C * (μ Set.univ).toReal = C

Tactic:
rw [this]

Tactic state after:
[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
 this : μ Set.univ = 1
 ⊢ C * ENNReal.toReal 1 = C]
import Mathlib
import FoML


open MeasureTheory ProbabilityTheory

theorem extracted_formal_statement_2.{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] {f : Ω → E} {C : ℝ}
  (h : ∀ᵐ (x : Ω) ∂μ, ‖f x‖ ≤ C) (this : μ Set.univ = 1) : C * ENNReal.toReal 1 = C := sorry

Tactic 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
this : μ Set.univ = 1
⊢ C * ENNReal.toReal 1 = C

Tactic:
simp

Tactic state after:
import Mathlib
import FoML


open MeasureTheory ProbabilityTheory

theorem extracted_formal_statement_3.{u_1} {Ω : Type u_1} [inst : MeasurableSpace Ω] {μ : Measure Ω}
  [inst_1 : IsProbabilityMeasure μ] {f : Ω → ℝ} {C : ℝ} (h : ∀ᵐ (x : Ω) ∂μ, |f x| ≤ C) :
  |∫ (x : Ω), f x ∂μ| ≤ C := sorry

Tactic state before:
Ω : Type u_1
inst✝¹ : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsProbabilityMeasure μ
f : Ω → ℝ
C : ℝ
h : ∀ᵐ (x : Ω) ∂μ, |f x| ≤ C
⊢ |∫ (x : Ω), f x ∂μ| ≤ C

Tactic:
exact @norm_expectation_le_of_norm_le_const Ω _ _ _ ℝ _ _ f C h

Tactic state after: