`BookProof.ChapterBayesInference.posterior_nonneg` (hprior : ∀ x, 0 ≤ prior x) (hL : ∀ x y, 0 ≤ L x y) (y : Y) (x : X) : 0 ≤ posterior prior L y x

Proved

BookProof.ChapterBayesInference.posterior_nonneg

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBayesInference.

BookProof.ChapterBayesInference.posterior_nonneg (hprior : ∀ x, 0 ≤ prior x) (hL : ∀ x y, 0 ≤ L x y) (y : Y) (x : X) : 0 ≤ posterior prior L y x

Formalization note: Lean 4 identifier BookProof.ChapterBayesInference.posterior_nonneg.

Preamble

-- Generated from ChapterBayesInference.lean — theorem BookProof.ChapterBayesInference.posterior_nonneg
import Mathlib
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference


open scoped BigOperators


variable {X Y : Type*} [Fintype X] [Fintype Y] [DecidableEq X] [DecidableEq Y]

variable {prior : X → ℝ} {L : X → Y → ℝ}

omit [Fintype Y] [DecidableEq X] [DecidableEq Y] in

Formal statement

theorem BookProof.ChapterBayesInference.posterior_nonneg (hprior : ∀ x, 0 ≤ prior x) (hL : ∀ x y, 0 ≤ L x y)
    (y : Y) (x : X) : 0 ≤ posterior prior L y x := by sorry

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