File size: 1,045 Bytes
dd14c26 | 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 | import OAI.Probability.MatroidProphet.Statements
import OAI.Probability.MatroidProphet.Gluing
import Mathlib.Tactic.NormNum
namespace OAI
open MeasureTheory ProbabilityTheory
namespace MatroidProphet
theorem hiddenVectorChallenge_implies_oneSampleChallenge.{u}
(hh : HiddenVectorChallenge) : OneSampleChallenge.{u} := by
intro n M hM
obtain ⟨bits, ν, hν, A, hA, hbound⟩ := hh n M hM
let := hν
refine ⟨bits, ν, hν, sampleSimulation A, sampleSimulation_feasible M A hA, ?_⟩
intro Ω mΩ μ hμ S V R hS hV hR hSN hVN hi hlaw hseed hRlaw hopt π hπ
obtain ⟨hri, hpay⟩ := oneSample_of_hidden M A ν (((2 : ℝ) ^ 293)⁻¹) hA hbound
μ S V R hS hV hR hSN hVN hi hlaw hseed hRlaw hopt π hπ
refine ⟨hri, le_trans ?_ hpay⟩
apply mul_le_mul_of_nonneg_right
· exact inv_anti₀ (pow_pos (by norm_num : (0 : ℝ) < 2) 293)
(pow_le_pow_right₀ (by norm_num : (1 : ℝ) ≤ 2) (by decide : 293 ≤ 310))
· exact integral_nonneg fun ω => optimum_nonneg M (V ω)
end MatroidProphet
end OAI
|