`BookProof.ChapterHierarchicalBayesComposition.idKernel_comp` (k : A → B → ℝ) : compKernel (idKernel : A → A → ℝ) k = k

Proved

BookProof.ChapterHierarchicalBayesComposition.idKernel_comp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHierarchicalBayesComposition.

BookProof.ChapterHierarchicalBayesComposition.idKernel_comp (k : A → B → ℝ) : compKernel (idKernel : A → A → ℝ) k = k

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

Preamble

-- Generated from ChapterHierarchicalBayesComposition.lean — theorem BookProof.ChapterHierarchicalBayesComposition.idKernel_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.idKernel_comp (k : A → B → ℝ) :
    compKernel (idKernel : A → A → ℝ) k = k := by sorry

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