`BookProof.ChapterUniformPriorPosterior.uniform_prior_posterior_eq` (q : Hyp → ℝ) (hq_sum : ∑ x, q x = 1) (c : ℝ) (hc : 0 < c) (x : Hyp) : BookProof.ChapterBayesInference.posterior

Proved

BookProof.ChapterUniformPriorPosterior.uniform_prior_posterior_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterUniformPriorPosterior.

BookProof.ChapterUniformPriorPosterior.uniform_prior_posterior_eq (q : Hyp → ℝ) (hq_sum : ∑ x, q x = 1) (c : ℝ) (hc : 0 < c) (x : Hyp) : BookProof.ChapterBayesInference.posterior (fun _ : Hyp => c) (binaryLikelihood q) true x = q x

Formalization note: Lean 4 identifier BookProof.ChapterUniformPriorPosterior.uniform_prior_posterior_eq.

Preamble

-- Generated from ChapterUniformPriorPosterior.lean — theorem BookProof.ChapterUniformPriorPosterior.uniform_prior_posterior_eq
import Mathlib
import Definitions.Def_ChapterUniformPriorPosterior
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference
open BookProof.ChapterUniformPriorPosterior


open scoped BigOperators


variable {Hyp : Type*} [Fintype Hyp] [DecidableEq Hyp]

Formal statement

theorem BookProof.ChapterUniformPriorPosterior.uniform_prior_posterior_eq (q : Hyp → ℝ) (hq_sum : ∑ x, q x = 1)
    (c : ℝ) (hc : 0 < c) (x : Hyp) :
    BookProof.ChapterBayesInference.posterior (fun _ : Hyp => c)
      (binaryLikelihood q) true x = q x := by sorry

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