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Explain the Lean theorem `ledgerAlg_id_left` in module `IndisputableMonolith.Algebra.RecognitionCategory`. 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.Algebra.RecognitionCategory does not contain any declaration named ledgerAlg_id_left. The module instead contains the theorem recAlg_id_left, which establishes the left unit law for morphism composition in the category RecAlg of cost algebras. Because the queried declaration name does not appear verbatim, no derivation of the requested theorem can be produced from the canon.

outside recognition

Aspects Recognition does not yet address:

  • ledgerAlg_id_left declaration
  • any theorem or definition using the exact name ledgerAlg_id_left

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.