`BookProof.ChapterBayesInference.joint_sum_one` (hprior_sum : ∑ x, prior x = 1) (hL_row : ∀ x, ∑ y, L x y = 1) : ∑ x, ∑ y, joint prior L x y = 1

Proved

BookProof.ChapterBayesInference.joint_sum_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBayesInference.

BookProof.ChapterBayesInference.joint_sum_one (hprior_sum : ∑ x, prior x = 1) (hL_row : ∀ x, ∑ y, L x y = 1) : ∑ x, ∑ y, joint prior L x y = 1

Formalization note: Lean 4 identifier BookProof.ChapterBayesInference.joint_sum_one.

Preamble

-- Generated from ChapterBayesInference.lean — theorem BookProof.ChapterBayesInference.joint_sum_one
import Mathlib
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference


open scoped BigOperators


variable {X Y : Type*} [Fintype X] [Fintype Y] [DecidableEq X] [DecidableEq Y]

variable {prior : X → ℝ} {L : X → Y → ℝ}

omit [DecidableEq X] [DecidableEq Y] in

Formal statement

theorem BookProof.ChapterBayesInference.joint_sum_one (hprior_sum : ∑ x, prior x = 1) (hL_row : ∀ x, ∑ y, L x y = 1) :
    ∑ x, ∑ y, joint prior L x y = 1 := by sorry

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