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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 | import OAI.Computability.PerfectCompleteness.Decoding.FixedStoppedUpperProbability
import OAI.Computability.PerfectCompleteness.Reduction.FixedStoppedContradiction
import OAI.Computability.PerfectCompleteness.Reduction.FixedStoppedPair
namespace OAI
section
namespace PerfectCompleteness.FixedPreliminarySoundness
noncomputable section
variable {δ : ℚ} {hδ : 0 < δ} (parameters : FixedParameters.Parameters δ hδ)
theorem no_large_strategy (input : List Bool)
(unsat : ¬ BinaryLanguage.language input)
(strategy : FixedPreliminaryGame.Strategy parameters input)
(hsuccess : InitialParameters.epsilon δ ≤
(FixedPreliminaryGame.game parameters input).success strategy) : False := by
obtain ⟨i, j, hij, hreserve⟩ := FixedStoppedPair.exists_pair parameters input strategy hsuccess
have hupper := FixedStoppedUpperProbability.meeting_ge_gamma
parameters i j hij input strategy hreserve
have hsmall := FixedStoppedContradiction.meeting_lt_gamma
parameters i j hij input strategy unsat
exact (not_lt_of_ge hupper) hsmall
end
end PerfectCompleteness.FixedPreliminarySoundness
end
end OAI
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