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a2ee19a | 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 | import OAI.Probability.MatroidProphet.Main
namespace OAI
namespace MatroidProphet
open MainAlgorithm
/-- The source safety guarantee, including the literal constants, all listed
groups, global independent comparison set, and the harmless unlisted zero case. -/
def SafeSampleClaim : Prop :=
∀ (n : ℕ) (M : Matroid (Fin n)) (hE : M.E = Set.univ)
(d : MainMasks n) (s : Fin n → Option ℤ) (i : ℤ)
(Y : Set (Fin n)), M.Indep Y →
exitThreshold / 4 *
((d.D : Set (Fin n)) ∩ (Y ∩ (trueGroup M d s i : Set (Fin n)))).ncard -
(d.D ∩ trueGroup M d s i).card / densityThreshold ≤
bitsExpectation (fun _ => thinningRate) Finset.univ (fun C =>
bitsExpectation (fun _ => thinningRate) Finset.univ (fun T =>
fairParityExpectation (fun p =>
(listedSafeStatistic M hE (2 ^ 100) (withMasks d d.D C T) s i Y
(boolParity p) : ℝ))))
end MatroidProphet
end OAI
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