`BookProof.ChapterUniformPriorPosterior.binaryLikelihood_nonneg` (q : Hyp → ℝ) (hq_nonneg : ∀ x, 0 ≤ q x) (hq_sum : ∑ x, q x = 1) (x : Hyp) (observed : Bool) : 0 ≤ binaryLikelihood

Proved

BookProof.ChapterUniformPriorPosterior.binaryLikelihood_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterUniformPriorPosterior.

BookProof.ChapterUniformPriorPosterior.binaryLikelihood_nonneg (q : Hyp → ℝ) (hq_nonneg : ∀ x, 0 ≤ q x) (hq_sum : ∑ x, q x = 1) (x : Hyp) (observed : Bool) : 0 ≤ binaryLikelihood q x observed

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

Preamble

-- Generated from ChapterUniformPriorPosterior.lean — theorem BookProof.ChapterUniformPriorPosterior.binaryLikelihood_nonneg
import Mathlib
import Definitions.Def_ChapterUniformPriorPosterior
open BookProof.ChapterUniformPriorPosterior


open scoped BigOperators


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

Formal statement

theorem BookProof.ChapterUniformPriorPosterior.binaryLikelihood_nonneg (q : Hyp → ℝ) (hq_nonneg : ∀ x, 0 ≤ q x)
    (hq_sum : ∑ x, q x = 1) (x : Hyp) (observed : Bool) :
    0 ≤ binaryLikelihood q x observed := by sorry

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