The supplied canon source does not contain the module IndisputableMonolith.Cost or any declaration named cosh_minus_one_eq. No Lean source for that module is provided, so the requested explanation of its formal statement, dependencies, or role cannot be given from the canon. The question asks specifically for an explanation of a lemma in a module absent from the supplied Recognition source.
Explain the Lean lemma `cosh_minus_one_eq` in module `IndisputableMonolith.Cost`. 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.
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outside recognition
- Module IndisputableMonolith.Cost
- Declaration cosh_minus_one_eq
- Any formal statement, proof, or dependencies for cosh_minus_one_eq
recognition modules consulted
IndisputableMonolith.Foundation.AlexanderDualityIndisputableMonolith.Mathematics.LanglandsFromRecognitionCostIndisputableMonolith.Foundation.RealityFromDistinctionIndisputableMonolith.Measurement.RSNative.Calibration.SingleAnchorIndisputableMonolith.Unification.RecognitionBandGeometryIndisputableMonolith.Unification.RecognitionBandwidthIndisputableMonolith.Foundation.RecognitionForcingIndisputableMonolith.Meta.ConstructiveNote