| import Mathlib |
| import OAI.Combinatorics.Chromatic.Walls.WallUnitNegative |
| import OAI.Combinatorics.Chromatic.Shuffle.RestrictionBGraded |
| import OAI.Combinatorics.Chromatic.Shuffle.SymbolInternalWeight |
| import OAI.Combinatorics.Chromatic.Shuffle.GradedShuffle |
| import OAI.Combinatorics.Chromatic.Walls.RootClosureFacts |
| import OAI.Combinatorics.Chromatic.Walls.MutationEventualIncoming |
| import OAI.Combinatorics.Chromatic.Walls.FiniteRefinementImport |
| import OAI.Combinatorics.Chromatic.Walls.GraphBlockPairing |
| import OAI.Combinatorics.Chromatic.Witness.ElementaryAlphabetRigidity |
|
|
| namespace OAI |
|
|
| section |
| namespace ElementaryPositivity.FiniteSearch |
| variable {n : ℕ} (G : NaturalUnitIntervalGraph n) |
|
|
| theorem exists_successful_table : ∃ t : Table n, Test G t := |
| exists_test G G.historyWitness |
|
|
| def selectedTable : Table n := Encodable.choose (exists_successful_table G) |
|
|
| theorem selectedTable_test : Test G (selectedTable G) := |
| Encodable.choose_spec (exists_successful_table G) |
|
|
| end ElementaryPositivity.FiniteSearch |
|
|
| def elementaryPositivityWitness (n : ℕ) |
| (G : ElementaryPositivity.NaturalUnitIntervalGraph n) : G.PermutationWitness where |
| theta σ := ElementaryPositivity.FiniteSearch.rowPartition |
| (ElementaryPositivity.FiniteSearch.selectedTable G σ.val) |
| expansion r := ElementaryPositivity.FiniteSearch.uniform_expansion_of_test |
| G G.historyWitness _ (ElementaryPositivity.FiniteSearch.selectedTable_test G) r |
|
|
| end |
|
|
| end OAI |
|
|
