lemma
proved
term proof
modally_equivalent_symm
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formal statement (Lean)
150lemma modally_equivalent_symm (c1 c2 : Config) :
151 modally_equivalent c1 c2 ↔ modally_equivalent c2 c1 := by
proof body
Term-mode proof.
152 simp [modally_equivalent]
153 constructor <;> (intro ⟨h1, h2, h3⟩; exact ⟨h1.symm, h3, h2⟩)
154
155/-- **MODAL NYQUIST THEOREM**: The universe cannot distinguish possibilities
156 finer than one tick.
157
158 This is the modal analog of:
159 - Nyquist sampling (time)
160 - Heisenberg uncertainty (phase space)
161 - Gap-45 consciousness threshold (qualia)
162
163 The 8-tick structure forces this limit. -/
depends on (22)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
-
tick
in IndisputableMonolith.Constants
decl_use
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tick
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
-
phase
in IndisputableMonolith.Foundation.EightTick
decl_use
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one
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
-
forces
in IndisputableMonolith.Foundation.MagnitudeOfMismatch
decl_use
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
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one
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
-
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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Config
in IndisputableMonolith.Gravity.ILG
decl_use
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
-
modally_equivalent
in IndisputableMonolith.Modal.ModalGeometry
decl_use
-
Config
in IndisputableMonolith.Modal.Possibility
decl_use
-
phase
in IndisputableMonolith.NumberTheory.RiemannHypothesis.Wedge
decl_use
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c1
in IndisputableMonolith.Physics.QCDRGE.MassAnomalousDimension
decl_use
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one
in IndisputableMonolith.QFT.SpinStatistics
decl_use
-
one
in IndisputableMonolith.RecogSpec.Core
decl_use