`BookProof.ChapterDeepLearningSampling.inducedPrior_supported` (seedProb : Seed → ℝ) (train : Seed → Model) (admissible : Model → Prop) (htrain : ∀ s, admissible (train s)) {m : Mo

Proved

BookProof.ChapterDeepLearningSampling.inducedPrior_supported

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDeepLearningSampling.

BookProof.ChapterDeepLearningSampling.inducedPrior_supported (seedProb : Seed → ℝ) (train : Seed → Model) (admissible : Model → Prop) (htrain : ∀ s, admissible (train s)) {m : Model} (hm : ¬ admissible m) : inducedPrior seedProb train m = 0

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

Preamble

-- Generated from ChapterDeepLearningSampling.lean — theorem BookProof.ChapterDeepLearningSampling.inducedPrior_supported
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.inducedPrior_supported (seedProb : Seed → ℝ) (train : Seed → Model)
    (admissible : Model → Prop)
    (htrain : ∀ s, admissible (train s)) {m : Model} (hm : ¬ admissible m) :
    inducedPrior seedProb train m = 0 := by sorry

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