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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 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | import OAI.LinearAlgebra.MatrixMultiplication.Entropy.BaseConditionalReaders
namespace OAI
/-! Dual matrix multiplication exponents and finite rectangular constructions. -/
noncomputable section
namespace MatrixMultiplication.DualWitness
attribute [local instance 10000] Classical.propDecidable Classical.decEq
attribute [local instance 11000] instDecidableEqFin
open MatrixMultiplication.Foundation RecursiveCompletion CompletionLabels
abbrev Word := Script.Coord (Fin 2) Script.dual
def source : FlaggedTensor Word Word Word := Script.tensor BaseTwo.flagged Script.dual
abbrev Support := RetainedLeaf source .B .C
def readable : ReadableTensor source :=
ReadableTensor.script BaseTwo.flagged BaseConditionalReaders.baseTwoReadable Script.dual
def program := terminationProgram source .B .C (by intro h; cases h)
readable.program readable.context_eq readable.view_eq
theorem program_complete : program.Complete :=
terminationProgram_complete source .B .C (by intro h; cases h)
readable.program readable.context_eq readable.view_eq readable.complete
theorem record_injective : Function.Injective
(labelRecordOf program.labels (1 + readable.depth)) :=
terminationRecord_injective source .B .C (by intro h; cases h)
readable.program readable.context_eq readable.view_eq readable.complete
def x (a : Support) : Word := a.val.val.1
theorem coord_card (U : Type*) [Fintype U] (s : Script) :
Fintype.card (Script.Coord U s) = Fintype.card U ^ s.factors := by
induction s with
| base =>
change Fintype.card U = Fintype.card U ^ 1
exact (pow_one _).symm
| step prior center m ih =>
change Fintype.card (Fin m → Script.Coord U prior) = _
simp only [Fintype.card_fun, Fintype.card_fin, ih, Script.factors, pow_mul]
theorem word_card : Fintype.card Word = 2 ^ 288 := by
simpa only [Fintype.card_fin, Script.dual_factors] using coord_card (Fin 2) Script.dual
end MatrixMultiplication.DualWitness
end
end OAI
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