import Mathlib.MeasureTheory.Order.Lattice
import Mathlib.Probability.Kernel.Basic
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.MeasureTheory.MeasurableSpace.Embedding
import Mathlib.Order.Restriction
import Mathlib.Probability.Kernel.IonescuTulcea.Maps
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic

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

set_option quotPrecheck false

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

-- ═══ 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

-- ═══ SequentialLearning.Algorithm ═══
section
open MeasureTheory ProbabilityTheory Filter Real Finset
open scoped ENNReal NNReal
namespace Learning
variable {𝓞 𝓐 𝓨 Ω : Type*} {m𝓞 : MeasurableSpace 𝓞} {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨} {mΩ : MeasurableSpace Ω}

/-- One round of interaction: an observation, then an action, then a feedback. -/
abbrev Round (𝓞 𝓐 𝓨 : Type*) := 𝓞 × 𝓐 × 𝓨

/-- History of `n` complete rounds; `n = 0` is the empty history. -/
abbrev Hist (𝓞 𝓐 𝓨 : Type*) (n : ℕ) := Fin n → Round 𝓞 𝓐 𝓨

/-- A stochastic environment.
At each round, an observation is drawn prior to the algorithm taking an action. Then the environment
provides feedback based on the observation and the action. -/
@[ext]
structure Environment (𝓞 𝓐 𝓨 : Type*) [MeasurableSpace 𝓞] [MeasurableSpace 𝓐] [MeasurableSpace 𝓨]
    where
  /-- Law of the observation of round `n` given the past rounds. -/
  obs : (n : ℕ) → Kernel (Hist 𝓞 𝓐 𝓨 n) 𝓞
  /-- Law of the feedback of round `n` given the past rounds, the observation and the action. -/
  feedback : (n : ℕ) → Kernel ((Hist 𝓞 𝓐 𝓨 n × 𝓞) × 𝓐) 𝓨
  /-- The observation kernel is a Markov kernel. -/
  [isMarkovKernel_obs : ∀ n, IsMarkovKernel (obs n)]
  /-- The feedback kernel is a Markov kernel. -/
  [isMarkovKernel_feedback : ∀ n, IsMarkovKernel (feedback n)]

instance (env : Environment 𝓞 𝓐 𝓨) (n : ℕ) : IsMarkovKernel (env.obs n) := env.isMarkovKernel_obs n

end Learning
end