`BookProof.ChapterFiniteBayesHierarchy.collapseKernels_append` (ks₁ ks₂ : List (S → S → ℝ)) : collapseKernels (ks₁ ++ ks₂) = compKernel (collapseKernels ks₁) (collapseKernels ks₂)

Proved

BookProof.ChapterFiniteBayesHierarchy.collapseKernels_append

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFiniteBayesHierarchy.

BookProof.ChapterFiniteBayesHierarchy.collapseKernels_append (ks₁ ks₂ : List (S → S → ℝ)) : collapseKernels (ks₁ ++ ks₂) = compKernel (collapseKernels ks₁) (collapseKernels ks₂)

Formalization note: Lean 4 identifier BookProof.ChapterFiniteBayesHierarchy.collapseKernels_append.

Preamble

-- Generated from ChapterFiniteBayesHierarchy.lean — theorem BookProof.ChapterFiniteBayesHierarchy.collapseKernels_append
import Mathlib
import Definitions.Def_ChapterFiniteBayesHierarchy
import Definitions.Def_ChapterHierarchicalBayesComposition
open BookProof.ChapterHierarchicalBayesComposition
open BookProof.ChapterFiniteBayesHierarchy


open scoped BigOperators


open BookProof.ChapterHierarchicalBayesComposition

variable {S : Type*} [Fintype S] [DecidableEq S]

Formal statement

theorem BookProof.ChapterFiniteBayesHierarchy.collapseKernels_append (ks₁ ks₂ : List (S → S → ℝ)) :
    collapseKernels (ks₁ ++ ks₂) =
      compKernel (collapseKernels ks₁) (collapseKernels ks₂) := by sorry

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