`BookProof.ChapterDutchBook.coherent_iff_exists_prob` [Fintype Ω] (Pr : Finset Ω → ℝ) : Coherent Pr ↔ ∃ p : Ω → ℝ, IsProb p ∧ Represents Pr p

Proved

BookProof.ChapterDutchBook.coherent_iff_exists_prob

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDutchBook.

BookProof.ChapterDutchBook.coherent_iff_exists_prob [Fintype Ω] (Pr : Finset Ω → ℝ) : Coherent Pr ↔ ∃ p : Ω → ℝ, IsProb p ∧ Represents Pr p

Formalization note: Lean 4 identifier BookProof.ChapterDutchBook.coherent_iff_exists_prob.

Preamble

-- Generated from ChapterDutchBook.lean — theorem BookProof.ChapterDutchBook.coherent_iff_exists_prob
import Mathlib
import Definitions.Def_ChapterDutchBook
open BookProof.ChapterDutchBook


open scoped BigOperators
open Finset


variable {Ω : Type*} [DecidableEq Ω]

Formal statement

theorem BookProof.ChapterDutchBook.coherent_iff_exists_prob [Fintype Ω] (Pr : Finset Ω → ℝ) :
    Coherent Pr ↔ ∃ p : Ω → ℝ, IsProb p ∧ Represents Pr p := by sorry

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