openAI-math-dataset / lean /OAI /RepresentationTheory /UniversalSquare /Contraction /CompactDomains.lean
| import Mathlib | |
| import OAI.RepresentationTheory.Saxl.Main | |
| import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools | |
| namespace OAI | |
| /-! Compact Domains. -/ | |
| section | |
| noncomputable section | |
| namespace UniversalTensorSquare | |
| open Saxl Saxl.Columns Saxl.Balance | |
| lemma rowSquare_compact {n : ℕ} {p q cs ts : List ℕ} | |
| (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) | |
| (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) | |
| (hn : cs.sum = n) (hn' : ts.sum = n) | |
| (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) | |
| (flag : Finset (ℕ × ℕ × ℕ)) | |
| (hcert : solveCompact n (.full ts) (.full cs) (.full cs) | |
| (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by | |
| apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag | |
| simpa only [← CompactDomains.describe_full,solveCompact_describe] using hcert | |
| end UniversalTensorSquare | |
| end | |
| end | |
| end OAI | |