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e3e0a0d | 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 44 45 46 47 48 49 50 51 52 53 54 55 56 | import Mathlib
import OAI.RepresentationTheory.Saxl.Main
import OAI.RepresentationTheory.UniversalSquare.Support.RowChecker
namespace OAI
/-! Fast Row Check. -/
section
namespace UniversalTensorSquare
def quickBand (M r : ℕ) (rs : List ℕ) : Bool :=
(List.range 4).any fun k =>
let d := k+1
let q := testWidth M d
decide (d*q+7+d ≤ 2*M-1) && decide (2*M-1 ≤ (rs.take d).sum) &&
decide (r ≤ ((List.range q).map fun j => (rs.countP (fun a => decide (j < a))-d)/2).sum)
lemma quickBand_sound {M r : ℕ} {rs : List ℕ} (h : quickBand M r rs = true) :
RowsBand M r rs := by
obtain ⟨k,hk,hh⟩ := List.any_eq_true.mp h
simp only [Bool.and_eq_true,decide_eq_true_eq] at hh
exact ⟨k,hk,hh.1.1,hh.1.2,hh.2⟩
def quickResidual (M r : ℕ) (qs : List (List ℕ)) (t : RowTree) (rs : List ℕ) : Bool :=
let ts := transposeRows rs
t.find rs || t.find ts || quickBand M r rs || quickBand M r ts ||
qs.any (fun q => decide (RowsDom rs q) || decide (RowsDom ts q))
lemma quickResidual_sound {M r : ℕ} {qs : List (List ℕ)} {t : RowTree} {rs : List ℕ}
(h : quickResidual M r qs t rs = true) : TreeResidual M r qs t rs := by
simp only [quickResidual,Bool.or_eq_true] at h
rcases h with (((h | h) | h) | h) | h
· exact Or.inr (Or.inl h)
· exact Or.inr (Or.inr h)
· exact Or.inl (Or.inl (quickBand_sound h))
· exact Or.inl (Or.inr (Or.inl (quickBand_sound h)))
· obtain ⟨q,hq,h⟩ := List.any_eq_true.mp h
simp only [Bool.or_eq_true,decide_eq_true_eq] at h
exact Or.inl (Or.inr (Or.inr (Or.inl ⟨q,hq,h⟩)))
lemma quickCheckedRows (M r : ℕ) (qs : List (List ℕ)) (t : RowTree)
(fuel n upper : ℕ) (A B : List (ℕ × ℕ))
(h : checkRowPrefixes (quickResidual M r qs t) fuel n upper A B [] = true) :
∀ rs ∈ constrainedRows fuel n upper A B, TreeResidual M r qs t rs := by
intro rs hrs
apply quickResidual_sound
simpa only [List.reverse_nil,List.nil_append] using
checkRowPrefixes_sound (quickResidual M r qs t) fuel n upper A B [] h rs hrs
end UniversalTensorSquare
end
end OAI
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