File size: 1,397 Bytes
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 28 29 30 31 32 | import OAI.Probability.MatroidProphet.Main
namespace OAI
namespace MatroidProphet
open Set Finset MeasureTheory
/-- Core and hidden prefix feasibility, measurability after masking the initial
observations, complete accepted-set nonanticipation, irrevocability, and literal
rejection of sacrificed labels. The mask depends only on the initial seed by
the type of `HiddenRule`; no weight-dependent mask is allowed. -/
def MainRuleFeasibility {n bits : ℕ} (M : Matroid (Fin n))
(A : HiddenRule n bits) : Prop :=
Feasible M A.core ∧
(∀ k, Measurable (fun x : Seed bits × (Weights n × History n k) =>
A.core.decide k x.1 (observed A x.1 x.2.1) x.2.2)) ∧
(∀ (w : Weights n), (∀ e, 0 ≤ w e) →
∀ (r : Seed bits) (π : ArrivalOrder n) (t : ℕ),
M.Indep (hiddenAcceptedThrough A r w π t : Set (Fin n))) ∧
(∀ (r : Seed bits) (w w' : Weights n) (π π' : ArrivalOrder n) (t : ℕ),
(∀ e ∈ A.mask r, w e = w' e) →
(∀ j : Fin n, j.val < t → (π j, w (π j)) = (π' j, w' (π' j))) →
hiddenAcceptedThrough A r w π t = hiddenAcceptedThrough A r w' π' t) ∧
(∀ (r : Seed bits) (w : Weights n) (π : ArrivalOrder n),
Monotone (hiddenAcceptedThrough A r w π)) ∧
(∀ (r : Seed bits) (w : Weights n) (π : ArrivalOrder n) (t : ℕ),
Disjoint (hiddenAcceptedThrough A r w π t) (A.mask r))
end MatroidProphet
end OAI
|