| import OAI.Dynamics.ConditionalShuffle.OverlayRate | |
| namespace OAI | |
| noncomputable section | |
| open scoped Classical | |
| namespace Revealed.Scheduled | |
| open Thorp Thorp.Conditional Thorp.Conditional.Hybrid Revealed.Split Revealed.Instrument Revealed.Disintegration | |
| variable {ι α : Type} [Fintype ι] [Fintype α] [DecidableEq α] | |
| lemma interval_cost_le (d t : ℕ) (σ : ℕ → Bool) (e : Outside ι α (Position d)) | |
| (c : (Equiv.Perm α → ℝ) → ℝ) (C : ℝ) | |
| (h : let μ := fairMass (fun ω : History d t => | |
| ((publicHistory (fun i : Fin t => σ i.val) ω, splitPath (sectionFrame e) t ω), | |
| assignment ((sectionFrame e).trans (run d t ω)))) | |
| ∑ p, marginal μ p * c (conditional μ p) ≤ C) | |
| : ∀ F : Fintype (Fin t → Symbol ι α d), | |
| .sum (Fin t → Symbol ι α d) ℝ _ (.univ _ F) | |
| (fun p => probability (interval d t σ) e p * c (kernel (interval d t σ) e p)) ≤ C := by | |
| let B : Fintype (Fin t → Symbol ι α d) := inferInstance | |
| have hh := (interval_weighted_cost d t σ e c).le.trans h | |
| intro F | |
| have hF : F = B := Subsingleton.elim _ _ | |
| rw [hF] | |
| exact hh | |
| end Revealed.Scheduled | |
| end | |
| end OAI | |