openAI-math-dataset / lean /OAI /RepresentationTheory /UniversalSquare /Support /SplitUnionRowChecker.lean
| 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 | |