`BookProof.ChapterDutchBook.Coherent.additive` {Pr : Finset Ω → ℝ} (h : Coherent Pr) {A B : Finset Ω} (hAB : Disjoint A B) : Pr (A ∪ B) = Pr A + Pr B

Proved

BookProof.ChapterDutchBook.Coherent.additive

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDutchBook.

BookProof.ChapterDutchBook.Coherent.additive {Pr : Finset Ω → ℝ} (h : Coherent Pr) {A B : Finset Ω} (hAB : Disjoint A B) : Pr (A ∪ B) = Pr A + Pr B

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

Preamble

-- Generated from ChapterDutchBook.lean — theorem BookProof.ChapterDutchBook.Coherent.additive
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.additive {Pr : Finset Ω → ℝ} (h : Coherent Pr)
    {A B : Finset Ω} (hAB : Disjoint A B) :
    Pr (A ∪ B) = Pr A + Pr B := by sorry

View graph