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cdec422 | 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 35 36 37 38 39 40 | 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
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