`BookProof.ChapterSequentialBayes.bayesUpdate_sum_one` {prior ℓ : X → ℝ} (hpos : 0 < totEvidence prior ℓ) : ∑ x, bayesUpdate prior ℓ x = 1

Proved

BookProof.ChapterSequentialBayes.bayesUpdate_sum_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSequentialBayes.

BookProof.ChapterSequentialBayes.bayesUpdate_sum_one {prior ℓ : X → ℝ} (hpos : 0 < totEvidence prior ℓ) : ∑ x, bayesUpdate prior ℓ x = 1

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

Preamble

-- Generated from ChapterSequentialBayes.lean — theorem BookProof.ChapterSequentialBayes.bayesUpdate_sum_one
import Mathlib
import Definitions.Def_ChapterSequentialBayes
open BookProof.ChapterSequentialBayes


open scoped BigOperators


variable {X : Type*} [Fintype X]

Formal statement

theorem BookProof.ChapterSequentialBayes.bayesUpdate_sum_one {prior ℓ : X → ℝ} (hpos : 0 < totEvidence prior ℓ) :
    ∑ x, bayesUpdate prior ℓ x = 1 := by sorry

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