`BookProof.ChapterPriorDependence.posterior_dirac` (a : Hyp) (L : Hyp → Data → ℝ) (d : Data) (ha : 0 < L a d) (x : Hyp) : BookProof.ChapterBayesInference.posterior (diracPrior a) L

Proved

BookProof.ChapterPriorDependence.posterior_dirac

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPriorDependence.

BookProof.ChapterPriorDependence.posterior_dirac (a : Hyp) (L : Hyp → Data → ℝ) (d : Data) (ha : 0 < L a d) (x : Hyp) : BookProof.ChapterBayesInference.posterior (diracPrior a) L d x = diracPrior a x

Formalization note: Lean 4 identifier BookProof.ChapterPriorDependence.posterior_dirac.

Preamble

-- Generated from ChapterPriorDependence.lean — theorem BookProof.ChapterPriorDependence.posterior_dirac
import Mathlib
import Definitions.Def_ChapterPriorDependence
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference
open BookProof.ChapterPriorDependence


open scoped BigOperators


variable {Hyp Data : Type*} [DecidableEq Hyp]

variable [Fintype Hyp]

Formal statement

theorem BookProof.ChapterPriorDependence.posterior_dirac (a : Hyp) (L : Hyp → Data → ℝ) (d : Data)
    (ha : 0 < L a d) (x : Hyp) :
    BookProof.ChapterBayesInference.posterior (diracPrior a) L d x =
      diracPrior a x := by sorry

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