Prove2Me

`BookProof.ChapterNoBestPrior.eq_of_expectedUtility_ge_all` (p q : Hyp → ℝ) (h : ∀ u : Hyp → ℝ, expectedUtility q u ≤ expectedUtility p u) : p = q

Proved
BookProof.ChapterNoBestPrior.eq_of_expectedUtility_ge_all

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNoBestPrior.

BookProof.ChapterNoBestPrior.eq_of_expectedUtility_ge_all (p q : Hyp → ℝ) (h : ∀ u : Hyp → ℝ, expectedUtility q u ≤ expectedUtility p u) : p = q

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

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


open scoped BigOperators


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

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