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`BookProof.ChapterBayesInference.evidence_eq_marginal` (y : Y) : evidence prior L y = ∑ x, joint prior L x y

Proved
BookProof.ChapterBayesInference.evidence_eq_marginal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBayesInference.

BookProof.ChapterBayesInference.evidence_eq_marginal (y : Y) : evidence prior L y = ∑ x, joint prior L x y

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

Preamble
-- Generated from ChapterBayesInference.lean — theorem BookProof.ChapterBayesInference.evidence_eq_marginal
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 [Fintype Y] [DecidableEq X] [DecidableEq Y] in
Formal statement
theorem BookProof.ChapterBayesInference.evidence_eq_marginal (y : Y) : evidence prior L y = ∑ x, joint prior L x y := by sorry

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