`BookProof.ChapterDeepLearningSampling.sum_inducedPrior_event` (seedProb : Seed → ℝ) (train : Seed → Model) (A : Finset Model) : ∑ m ∈ A, inducedPrior seedProb train m = ∑ s with t

Proved

BookProof.ChapterDeepLearningSampling.sum_inducedPrior_event

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDeepLearningSampling.

BookProof.ChapterDeepLearningSampling.sum_inducedPrior_event (seedProb : Seed → ℝ) (train : Seed → Model) (A : Finset Model) : ∑ m ∈ A, inducedPrior seedProb train m = ∑ s with train s ∈ A, seedProb s

Formalization note: Lean 4 identifier BookProof.ChapterDeepLearningSampling.sum_inducedPrior_event.

Preamble

-- Generated from ChapterDeepLearningSampling.lean — theorem BookProof.ChapterDeepLearningSampling.sum_inducedPrior_event
import Mathlib
import Definitions.Def_ChapterDeepLearningSampling
open BookProof.ChapterDeepLearningSampling


open scoped BigOperators


variable {Seed Model Data : Type*}
variable [Fintype Seed] [DecidableEq Model]

Formal statement

theorem BookProof.ChapterDeepLearningSampling.sum_inducedPrior_event
    (seedProb : Seed → ℝ) (train : Seed → Model)
    (A : Finset Model) :
    ∑ m ∈ A, inducedPrior seedProb train m = ∑ s with train s ∈ A, seedProb s := by sorry

View graph