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KRF.star_kb

Disproved
KRF.star_kb

by jario · Sep 7, 2026 · Mathlib c5ea003 (Lean v4.30.0)

Milestone statement KRF.star_kb of the arXiv 2412.11855 formalization campaign: see the source reference theorem.

Preamble
/-
Lemma (paper lem:star_kb, appendix proof): 𝕂(M*) = cl(𝕂(M)) for every QA
engine M. This is the defining semantic property of Procedure 1 (Alg 1) — the
task-array construction of the six-part computation. Proof (by induction on
the closure sequence, in the paper's appendix) is out of scope for this stage;
it is the milestone's content.
-/
import Definitions.Def_KRF_Machinery

noncomputable section

open KRFCore

namespace KRF

variable {σD σQ : Sig}
Formal statement
theorem star_kb {Q : QueryLanguage σQ} (S : StarContract σD σQ Q) (M : QAEngine σD σQ) :
    ∀ D φ, KM (S.star M) D φ ↔ Closure Q (KM M) D φ := by
  sorry

end KRF
Source
arXiv 2412.11855v2 (Zhang, Jiang, Quan)

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