The supplied Lean source for module IndisputableMonolith.Algebra.CostAlgebra contains no declaration named equivFinTwo (or any variant). The module defines the J-cost function (J), the Recognition Composition Law (SatisfiesRCL, RCL_holds), cost composition (costCompose, ★), shifted monoids on [1/2, ∞) and [1, ∞) (ShiftedCarrier, ShiftedHValue, shiftedCompose), defect distance (defectDist), and supporting theorems such as J_at_one, J_reciprocal, J_nonneg, J_defect_form, costCompose_comm, costCompose_assoc_defect, H_dAlembert, defectDist_self, defectDist_symm, defectDist_nonneg, defectDist_quasi_triangle_local, and costCompose_no_identity. No equivalence, isomorphism, or definition involving Fin 2 (or Fin.two) appears. The question therefore cannot be answered from the canon.
Explain the Lean def `equivFinTwo` in module `IndisputableMonolith.Algebra.CostAlgebra`. 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
- The definition `equivFinTwo` (or any equivalent) in IndisputableMonolith.Algebra.CostAlgebra
- Any plain-English description, Recognition Science role, formal reading, dependencies, or non-proofs for `equivFinTwo`
recognition modules consulted
IndisputableMonolith.Foundation.AlexanderDualityIndisputableMonolith.Algebra.CostAlgebraIndisputableMonolith.Mathematics.LanglandsFromRecognitionCostIndisputableMonolith.Foundation.RealityFromDistinctionIndisputableMonolith.Measurement.RSNative.Calibration.SingleAnchorIndisputableMonolith.Unification.RecognitionBandGeometryIndisputableMonolith.Unification.RecognitionBandwidthIndisputableMonolith.Algebra.RecognitionCategory