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Explain the Lean lemma `taylorWithinEval_two_univ` in module `IndisputableMonolith.Cost.FunctionalEquation`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: low outside recognition cached

The supplied Lean source for module IndisputableMonolith.Cost.FunctionalEquation contains multiple declarations establishing properties of the J-cost functional equation and related d'Alembert identities (e.g., Jcost_G_eq_cosh_sub_one, Jcost_cosh_add_identity, dAlembert_even, dAlembert_double). However, the specific declaration taylorWithinEval_two_univ does not appear in the provided source text for this module or any other module. The module imports Mathlib.Analysis.Calculus.Taylor but does not define or prove the named lemma internally.

outside recognition

Aspects Recognition does not yet address:

  • taylorWithinEval_two_univ declaration in IndisputableMonolith.Cost.FunctionalEquation

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.