`BookProof.ChapterSequentialBayes.bayesUpdate_nonneg` {prior ℓ : X → ℝ} (hprior : ∀ x, 0 ≤ prior x) (hℓ : ∀ x, 0 ≤ ℓ x) (x : X) : 0 ≤ bayesUpdate prior ℓ x

Proved

BookProof.ChapterSequentialBayes.bayesUpdate_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSequentialBayes.

BookProof.ChapterSequentialBayes.bayesUpdate_nonneg {prior ℓ : X → ℝ} (hprior : ∀ x, 0 ≤ prior x) (hℓ : ∀ x, 0 ≤ ℓ x) (x : X) : 0 ≤ bayesUpdate prior ℓ x

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

Preamble

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


open scoped BigOperators


variable {X : Type*} [Fintype X]

Formal statement

theorem BookProof.ChapterSequentialBayes.bayesUpdate_nonneg {prior ℓ : X → ℝ} (hprior : ∀ x, 0 ≤ prior x)
    (hℓ : ∀ x, 0 ≤ ℓ x) (x : X) : 0 ≤ bayesUpdate prior ℓ x := by sorry

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