`BookProof.ChapterDeepLearningSampling.posterior_eq_zero_of_not_mem_range` (seedProb : Seed → ℝ) (train : Seed → Model) (likelihood : Model → Data → ℝ) (d : Data) {m : Model} (hm :

Proved

BookProof.ChapterDeepLearningSampling.posterior_eq_zero_of_not_mem_range

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDeepLearningSampling.

BookProof.ChapterDeepLearningSampling.posterior_eq_zero_of_not_mem_range (seedProb : Seed → ℝ) (train : Seed → Model) (likelihood : Model → Data → ℝ) (d : Data) {m : Model} (hm : m ∉ Set.range train) : posterior seedProb train likelihood d m = 0

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

Preamble

-- Generated from ChapterDeepLearningSampling.lean — theorem BookProof.ChapterDeepLearningSampling.posterior_eq_zero_of_not_mem_range
import Mathlib
import Definitions.Def_ChapterDeepLearningSampling
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference
open BookProof.ChapterDeepLearningSampling


open scoped BigOperators


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








variable [Fintype Model]

Formal statement

theorem BookProof.ChapterDeepLearningSampling.posterior_eq_zero_of_not_mem_range (seedProb : Seed → ℝ)
    (train : Seed → Model) (likelihood : Model → Data → ℝ) (d : Data)
    {m : Model} (hm : m ∉ Set.range train) :
    posterior seedProb train likelihood d m = 0 := by sorry

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