import Mathlib.MeasureTheory.Order.Lattice
import Mathlib.Probability.Independence.Integration
import Mathlib.Probability.Kernel.Representation
import Mathlib.Probability.Kernel.IonescuTulcea.Traj
import Mathlib.Probability.Process.FiniteDimensionalLaws
import Mathlib.Probability.HasCondDistrib
import Mathlib.MeasureTheory.Measure.ProbabilityMeasure
import Mathlib.Probability.Independence.Basic
import Mathlib.Probability.Independence.Conditional
import Mathlib.MeasureTheory.Measure.SubFinite
import Mathlib.Probability.Kernel.RadonNikodym
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.Probability.Kernel.Composition.MapComap
import Mathlib.Order.CompletePartialOrder
import Mathlib.Probability.Martingale.BorelCantelli
import Mathlib.Probability.IdentDistrib
import Mathlib.Probability.Independence.InfinitePi
import Mathlib.MeasureTheory.Function.FactorsThrough

/-! # Standalone extraction for `hasLaw_eval_infinitePi`
Definitions are copied verbatim; theorem proofs are replaced by `sorry`.
Auto-generated by Referee. -/

set_option quotPrecheck false

-- Namespace stubs (so later `open`s resolve).
namespace Finset
end Finset
namespace MeasureTheory
end MeasureTheory
namespace ProbabilityTheory
end ProbabilityTheory
namespace Learning
end Learning
namespace ENNReal
end ENNReal
namespace Bandits
end Bandits

-- ═══ ForMathlib.MeasureTheory.Order.Lattice ═══
section
open Finset
variable {α δ : Type*} [MeasurableSpace δ] [SemilatticeInf α] {m : MeasurableSpace α} [MeasurableInf₂ α]
attribute [to_dual existing] MeasurableInf₂
end

-- ═══ Online.Bandit.ArrayProbSpace ═══
section
open MeasureTheory ProbabilityTheory Filter Real Finset Learning
open scoped ENNReal NNReal
namespace Bandits
variable {𝓐 R : Type*} {m𝓐 : MeasurableSpace 𝓐} {mR : MeasurableSpace R}
section MeasureSpace
section StreamMeasure

lemma _root_.hasLaw_eval_infinitePi {ι : Type*} {X : ι → Type*} {mX : ∀ i, MeasurableSpace (X i)}
  (μ : (i : ι) → Measure (X i)) [hμ : ∀ i, IsProbabilityMeasure (μ i)] (i : ι) :
    HasLaw (Function.eval i) (μ i) (Measure.infinitePi μ) := sorry

end StreamMeasure
end MeasureSpace
end Bandits
end