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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 | import Mathlib
import OAI.RepresentationTheory.Saxl.Main
import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker
namespace OAI
/-! Split Union Row Checker. -/
section
namespace UniversalTensorSquare
lemma checkRegionPrefixes_step (P : List ℕ → Bool) (k n upper : ℕ)
(regions : List PrefixRegion) (pref : List ℕ)
(hc : ∀ a, max 1 (n/(k+1)) ≤ a → a ≤ min n upper → n ≤ (k+1)*a →
checkRegionPrefixes P k (n-a) a
(nextRegions a (liveRegions (k+1) n upper regions)) (a::pref) = true) :
checkRegionPrefixes P (k+1) n upper regions pref = true := by
rw [checkRegionPrefixes]
split_ifs with hnone
· rfl
· apply List.all_eq_true.mpr
intro a ha
have ha' := List.mem_range'_1.mp ha
split_ifs with hn
· apply hc a ha'.1 ?_ hn
omega
· rfl
end UniversalTensorSquare
end
end OAI
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