`BookProof.ChapterDutchBook.payoff_single` (Pr : Finset Ω → ℝ) (A₀ : Finset Ω) (s₀ : ℝ) (ω : Ω) : payoff Pr ![A₀] ![s₀] ω = s₀ * (betIndicator A₀ ω - Pr A₀)

Proved

BookProof.ChapterDutchBook.payoff_single

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDutchBook.

BookProof.ChapterDutchBook.payoff_single (Pr : Finset Ω → ℝ) (A₀ : Finset Ω) (s₀ : ℝ) (ω : Ω) : payoff Pr ![A₀] ![s₀] ω = s₀ * (betIndicator A₀ ω - Pr A₀)

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

Preamble

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


open scoped BigOperators
open Finset


variable {Ω : Type*} [DecidableEq Ω]

Formal statement

theorem BookProof.ChapterDutchBook.payoff_single (Pr : Finset Ω → ℝ) (A₀ : Finset Ω) (s₀ : ℝ) (ω : Ω) :
    payoff Pr ![A₀] ![s₀] ω = s₀ * (betIndicator A₀ ω - Pr A₀) := by sorry

View graph