`BookProof.ChapterSequentialBayes.posterior_eq_bayesUpdate` {Y : Type*} (prior : X → ℝ) (L : X → Y → ℝ) (y : Y) : BookProof.ChapterBayesInference.posterior prior L y = bayesUpdate

Proved

BookProof.ChapterSequentialBayes.posterior_eq_bayesUpdate

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSequentialBayes.

BookProof.ChapterSequentialBayes.posterior_eq_bayesUpdate {Y : Type*} (prior : X → ℝ) (L : X → Y → ℝ) (y : Y) : BookProof.ChapterBayesInference.posterior prior L y = bayesUpdate prior (fun x => L x y)

Formalization note: Lean 4 identifier BookProof.ChapterSequentialBayes.posterior_eq_bayesUpdate.

Preamble

-- Generated from ChapterSequentialBayes.lean — theorem BookProof.ChapterSequentialBayes.posterior_eq_bayesUpdate
import Mathlib
import Definitions.Def_ChapterSequentialBayes
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference
open BookProof.ChapterSequentialBayes


open scoped BigOperators


variable {X : Type*} [Fintype X]

Formal statement

theorem BookProof.ChapterSequentialBayes.posterior_eq_bayesUpdate {Y : Type*}
    (prior : X → ℝ) (L : X → Y → ℝ) (y : Y) :
    BookProof.ChapterBayesInference.posterior prior L y = bayesUpdate prior (fun x => L x y) := by sorry

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