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cdec422 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | import OAI.LinearAlgebra.MatrixMultiplication.Duality.WitnessEntropy
import OAI.LinearAlgebra.MatrixMultiplication.Duality.ScriptIndependence
import OAI.LinearAlgebra.MatrixMultiplication.Duality.TerminationIndependence
import OAI.LinearAlgebra.MatrixMultiplication.Duality.InformationSchedule
namespace OAI
/-! Dual matrix multiplication exponents and finite rectangular constructions. -/
noncomputable section
namespace MatrixMultiplication.DualWitnessRates
attribute [local instance 10000] Classical.propDecidable Classical.decEq
attribute [local instance 11000] instDecidableEqFin
open MatrixMultiplication.Foundation CompletionLabels CompletionLabels.TopologicalFlatten
open DualInformation DualCompletionLaws DualWitness
theorem nonincident_independent (n : Fin (1 + readable.depth))
(hn : program.pair n.val = .yz) :
ConditionalIndependent law (labelRecordOf program.labels n.val)
(program.labels n.val) x := by
exact DualProgramIndependence.termination_independent source readable laws288
state288.rho
(by rw [state288_rho]; exact rho288_range.1.le)
(by rw [state288_rho]; exact rho288_range.2.le)
DualProgramIndependence.laws288_independent n hn
theorem incident_rate : rate .xy + rate .xz = 288 * Real.log 2 := by
let : Fintype (Coordinate Word Word Word .B) := inferInstanceAs (Fintype Word)
have h := program.incident_rate_eq_x_entropy law program_complete PUnit.unit
(fun _ => rfl) (fun n hn => nonincident_independent n hn)
change rate .xy + rate .xz = finiteEntropy (law.map x).mass at h
rw [x_entropy] at h
exact h
theorem hidden_rate : rate .yz = 288 * hiddenRate := by
linarith only [rate_sum, law_entropy, incident_rate]
end MatrixMultiplication.DualWitnessRates
end
end OAI
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