openAI-math-dataset / lean /OAI /LinearAlgebra /MatrixMultiplication /FieldParameters /Traversal.lean
| import OAI.LinearAlgebra.MatrixMultiplication.FieldParameters.Distributions | |
| namespace OAI | |
| /-! Fixed rational distributions and their entropy and capacity formulas. -/ | |
| namespace MatrixMultiplication.AllFieldParameters | |
| def placements (s : Shape) : List Shape := | |
| [shape (s 0) (s 1) (s 2), shape (s 0) (s 2) (s 1), | |
| shape (s 1) (s 0) (s 2), shape (s 1) (s 2) (s 0), | |
| shape (s 2) (s 0) (s 1), shape (s 2) (s 1) (s 0)] | |
| theorem initialMultiplicity_counts_placements : ∀ s ∈ sortedInitial, | |
| (placements s).eraseDups.length = initialMultiplicity s := by decide +kernel | |
| theorem parents_nodup : sortedInitial.Nodup ∧ positiveInitial.Nodup ∧ | |
| positiveSecond.Nodup ∧ zeroSecond.Nodup := by decide +kernel | |
| theorem split_keys_nodup : (splitKeys positiveInitial).Nodup ∧ | |
| (splitKeys positiveSecond).Nodup := by decide +kernel | |
| theorem binary_keys_nodup : binaryKeys.Nodup := by decide +kernel | |
| theorem pair_keys_nodup : pairKeys.Nodup := by decide +kernel | |
| theorem stageA_children_nodup : ∀ s ∈ positiveInitial, (below s).Nodup := by decide +kernel | |
| theorem stageB_children_nodup : ∀ s ∈ positiveSecond, (below s).Nodup := by decide +kernel | |
| theorem ordered_pairs_nodup : ∀ t ∈ zeroSecond, (orderedPairs t).Nodup := by decide +kernel | |
| theorem initial_placements_partition : | |
| (sortedInitial.flatMap (fun s => (placements s).eraseDups)).Perm (shapes 16) := by | |
| decide +kernel | |
| end MatrixMultiplication.AllFieldParameters | |
| end OAI | |