`BookProof.ChapterFiniteArithmeticPrior.prior_is_probability` {B : ℕ} {H : Type*} [Fintype H] (E : BayesianArithmeticExtension B H) : (∀ h, 0 ≤ E.prior h) ∧ ∑ h, E.prior h = 1

Proved

BookProof.ChapterFiniteArithmeticPrior.prior_is_probability

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFiniteArithmeticPrior.

BookProof.ChapterFiniteArithmeticPrior.prior_is_probability {B : ℕ} {H : Type*} [Fintype H] (E : BayesianArithmeticExtension B H) : (∀ h, 0 ≤ E.prior h) ∧ ∑ h, E.prior h = 1

Formalization note: Lean 4 identifier BookProof.ChapterFiniteArithmeticPrior.prior_is_probability.

Preamble

-- Generated from ChapterFiniteArithmeticPrior.lean — theorem BookProof.ChapterFiniteArithmeticPrior.prior_is_probability
import Mathlib
import Definitions.Def_ChapterFiniteArithmeticPrior
open BookProof.ChapterFiniteArithmeticPrior

Formal statement

theorem BookProof.ChapterFiniteArithmeticPrior.prior_is_probability {B : ℕ} {H : Type*} [Fintype H]
    (E : BayesianArithmeticExtension B H) :
    (∀ h, 0 ≤ E.prior h) ∧ ∑ h, E.prior h = 1 := by sorry

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