Prove2Me

`BookProof.ChapterNoBestPrior.not_uniformly_better` (p q : Hyp → ℝ) (hpq : p ≠ q) : ¬ ∀ u : Hyp → ℝ, expectedUtility q u ≤ expectedUtility p u

Proved
BookProof.ChapterNoBestPrior.not_uniformly_better

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNoBestPrior.

BookProof.ChapterNoBestPrior.not_uniformly_better (p q : Hyp → ℝ) (hpq : p ≠ q) : ¬ ∀ u : Hyp → ℝ, expectedUtility q u ≤ expectedUtility p u

Formalization note: Lean 4 identifier BookProof.ChapterNoBestPrior.not_uniformly_better.

Preamble
-- Generated from ChapterNoBestPrior.lean — theorem BookProof.ChapterNoBestPrior.not_uniformly_better
import Mathlib
import Definitions.Def_ChapterNoBestPrior
open BookProof.ChapterNoBestPrior


open scoped BigOperators


variable {Hyp : Type*} [Fintype Hyp]
Formal statement
theorem BookProof.ChapterNoBestPrior.not_uniformly_better (p q : Hyp → ℝ) (hpq : p ≠ q) :
    ¬ ∀ u : Hyp → ℝ, expectedUtility q u ≤ expectedUtility p u := by sorry

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