`BookProof.ChapterDutchBook.payoff_triple` (Pr : Finset Ω → ℝ) (A₀ A₁ A₂ : Finset Ω) (s₀ s₁ s₂ : ℝ) (ω : Ω) : payoff Pr ![A₀, A₁, A₂] ![s₀, s₁, s₂] ω = s₀ *...

Proved

BookProof.ChapterDutchBook.payoff_triple

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDutchBook.

BookProof.ChapterDutchBook.payoff_triple (Pr : Finset Ω → ℝ) (A₀ A₁ A₂ : Finset Ω) (s₀ s₁ s₂ : ℝ) (ω : Ω) : payoff Pr ![A₀, A₁, A₂] ![s₀, s₁, s₂] ω = s₀ * (betIndicator A₀ ω - Pr A₀) + s₁ * (betIndicator A₁ ω - Pr A₁) + s₂ * (betIndicator A₂ ω - Pr A₂)

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

Preamble

-- Generated from ChapterDutchBook.lean — theorem BookProof.ChapterDutchBook.payoff_triple
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_triple (Pr : Finset Ω → ℝ) (A₀ A₁ A₂ : Finset Ω)
    (s₀ s₁ s₂ : ℝ) (ω : Ω) :
    payoff Pr ![A₀, A₁, A₂] ![s₀, s₁, s₂] ω =
      s₀ * (betIndicator A₀ ω - Pr A₀) + s₁ * (betIndicator A₁ ω - Pr A₁)
        + s₂ * (betIndicator A₂ ω - Pr A₂) := by sorry

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