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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 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | import OAI.Probability.MatroidProphet.Main
namespace OAI
/-! The source writes the accounting sacrifice set as `D ∪ C`, whereas the
implementation retains `H ∪ D ∪ C`. Every candidate is outside H, so these
expressions agree on every actual nominal layer, before taking any rank. -/
namespace MatroidProphet.MainAlgorithm
open Set Finset
variable {n : ℕ}
lemma groupMask_not_mem_filter (M : Matroid (Fin n)) (d : MainMasks n)
(w : Fin n → Option ℤ) (mask : Finset (Fin n)) (h : ℕ) {e : Fin n}
(he : e ∈ groupMask M d w mask h) : e ∉ d.H := he.2.1.2.1
lemma nominalLayer_sacrifice_eq_source (M : Matroid (Fin n)) (hE : M.E = Set.univ)
(d : MainMasks n) (w : Fin n → Option ℤ) (h : ℕ) (ε : Fin 2)
(b : Pivots.ParityWindow (activation h) ε) :
nominalLayerSet M hE (2^100) (groupMask M d w d.D) (groupMask M d w d.C)
h (groupMask M d w univ h) ε b \ ((d.H ∪ d.D ∪ d.C : Finset (Fin n)) : Set (Fin n)) =
nominalLayerSet M hE (2^100) (groupMask M d w d.D) (groupMask M d w d.C)
h (groupMask M d w univ h) ε b \ ((d.D ∪ d.C : Finset (Fin n)) : Set (Fin n)) := by
ext e
constructor
· rintro ⟨he, hnot⟩
refine ⟨he, ?_⟩
intro heO
exact hnot (by
simp only [Finset.mem_coe, Finset.mem_union] at heO ⊢
tauto)
· rintro ⟨he, hnot⟩
have heG := nominalLayerSet_subset M hE (2^100)
(groupMask M d w d.D) (groupMask M d w d.C) h (groupMask M d w univ h) ε b he
have heH := groupMask_not_mem_filter M d w univ h heG
refine ⟨he, ?_⟩
simp only [Finset.mem_coe, Finset.mem_union] at hnot ⊢
tauto
end MatroidProphet.MainAlgorithm
end OAI
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