| 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 |
|
|
