`BookProof.ChapterDutchBook.Coherent.represents_singleton` {Pr : Finset Ω → ℝ} (h : Coherent Pr) (A : Finset Ω) : Pr A = ∑ ω ∈ A, Pr {ω}

Proved

BookProof.ChapterDutchBook.Coherent.represents_singleton

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDutchBook.

BookProof.ChapterDutchBook.Coherent.represents_singleton {Pr : Finset Ω → ℝ} (h : Coherent Pr) (A : Finset Ω) : Pr A = ∑ ω ∈ A, Pr {ω}

Formalization note: Lean 4 identifier BookProof.ChapterDutchBook.Coherent.represents_singleton.

Preamble

-- Generated from ChapterDutchBook.lean — theorem BookProof.ChapterDutchBook.Coherent.represents_singleton
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.represents_singleton {Pr : Finset Ω → ℝ} (h : Coherent Pr)
    (A : Finset Ω) : Pr A = ∑ ω ∈ A, Pr {ω} := by sorry

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