`BookProof.ChapterObservableExpectation.bayesPosterior_nonneg` {prior : Fin m → ℝ} {L : Fin m → Y → ℝ} (hprior : ∀ x, 0 ≤ prior x) (hL : ∀ x y, 0 ≤ L x y) (y : Y) (x : Fin m) : 0 ≤

Proved

BookProof.ChapterObservableExpectation.bayesPosterior_nonneg

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterObservableExpectation.

BookProof.ChapterObservableExpectation.bayesPosterior_nonneg {prior : Fin m → ℝ} {L : Fin m → Y → ℝ} (hprior : ∀ x, 0 ≤ prior x) (hL : ∀ x y, 0 ≤ L x y) (y : Y) (x : Fin m) : 0 ≤ posterior prior L y x

Formalization note: Lean 4 identifier BookProof.ChapterObservableExpectation.bayesPosterior_nonneg.

Preamble

-- Generated from ChapterObservableExpectation.lean — theorem BookProof.ChapterObservableExpectation.bayesPosterior_nonneg
import Definitions.Def_ChapterSoftmaxBorn
import Mathlib
import Definitions.Def_ChapterObservableExpectation
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference
open BookProof.ChapterObservableExpectation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxBorn

variable {m n : ℕ}
variable {E : Type*} [AddCommGroup E] [Module ℝ E]

variable {Y : Type*}

Formal statement

theorem BookProof.ChapterObservableExpectation.bayesPosterior_nonneg {prior : Fin m → ℝ} {L : Fin m → Y → ℝ}
    (hprior : ∀ x, 0 ≤ prior x) (hL : ∀ x y, 0 ≤ L x y) (y : Y) (x : Fin m) :
    0 ≤ posterior prior L y x := by sorry

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