| 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 |
|
|
