File size: 1,168 Bytes
92416a2 | 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 | 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),
@Finset.sum (Fin t → Symbol ι α d) ℝ _ (@Finset.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
|