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2f887db | 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 | import OAI.Computability.PerfectCompleteness.Decoding.DecoderFamilyLawLemmas
import OAI.Computability.PerfectCompleteness.Reduction.FixedStoppedHighBound
namespace OAI
section
namespace PerfectCompleteness.FixedStoppedContradiction
noncomputable section
attribute [local instance] FixedStoppedDecoderLaw.sampleFintype
UniqueGamesTheorem.Appendix.RankLevelFilter.linearMapFintype
variable {δ : ℚ} {hδ : 0 < δ} (parameters : FixedParameters.Parameters δ hδ)
(i j : Fin parameters.plan.depth) (hij : i < j) (input : List Bool)
theorem meeting_lt_gamma
(strategy : FixedPreliminaryGame.Strategy parameters input)
(unsat : ¬BinaryLanguage.language input) :
(FixedStoppedDecoderLaw.law parameters i j hij input strategy).probability
(FixedStoppedDecoderLaw.meeting parameters i j hij input) <
FixedRankContradiction.gamma parameters (j.val + 1) := by
apply lt_of_not_ge
intro hupper
exact FixedDecoderFamilyContradiction.impossible parameters
(FixedStoppedDecoderContext.geometry parameters i j hij input) input
(FixedStoppedDecoderLaw.labeling parameters input strategy)
(FixedStoppedDecoderLaw.useful parameters i j hij input strategy)
parameters.plan.order parameters.plan.density
(FixedStoppedDecoderContext.advice parameters i j hij input)
(FixedStoppedDecoderContext.direction parameters i j hij input)
(FixedStoppedDecoderLaw.threshold parameters j)
(FixedStoppedDecoderContext.law parameters i j hij input)
unsat (le_refl _) parameters.plan.density_pos
(j.val + 1) (Nat.succ_le_of_lt j.isLt) hupper
(FixedStoppedHighBound.probability_square_le parameters i j hij input strategy)
end
end PerfectCompleteness.FixedStoppedContradiction
end
end OAI
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