`BookProof.ChapterHierarchicalBayesComposition.terminalMarginal_comp` (k₁ : A → B → ℝ) (k₂ : B → C → ℝ) (likelihood : C → ℝ) : terminalMarginal k₁ (terminalMarginal k₂...

Proved

BookProof.ChapterHierarchicalBayesComposition.terminalMarginal_comp

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHierarchicalBayesComposition.

BookProof.ChapterHierarchicalBayesComposition.terminalMarginal_comp (k₁ : A → B → ℝ) (k₂ : B → C → ℝ) (likelihood : C → ℝ) : terminalMarginal k₁ (terminalMarginal k₂ likelihood) = terminalMarginal (compKernel k₁ k₂) likelihood

Formalization note: Lean 4 identifier BookProof.ChapterHierarchicalBayesComposition.terminalMarginal_comp.

Preamble

-- Generated from ChapterHierarchicalBayesComposition.lean — theorem BookProof.ChapterHierarchicalBayesComposition.terminalMarginal_comp
import Mathlib
import Definitions.Def_ChapterHierarchicalBayesComposition
open BookProof.ChapterHierarchicalBayesComposition


open scoped BigOperators


variable {A B C D : Type*}
  [Fintype A] [Fintype B] [Fintype C] [Fintype D]
  [DecidableEq A] [DecidableEq B] [DecidableEq C] [DecidableEq D]

Formal statement

theorem BookProof.ChapterHierarchicalBayesComposition.terminalMarginal_comp (k₁ : A → B → ℝ) (k₂ : B → C → ℝ)
    (likelihood : C → ℝ) :
    terminalMarginal k₁ (terminalMarginal k₂ likelihood) =
      terminalMarginal (compKernel k₁ k₂) likelihood := by sorry

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