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ae00908 | 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 | import OAI.Algebra.FormulaHitting.Specification
import OAI.Algebra.FormulaHitting.Program
import OAI.Algebra.FormulaHitting.GeneratorCost
import OAI.Algebra.FormulaHitting.OutputBounds
import OAI.Algebra.FormulaHitting.BitCost
namespace OAI
namespace NCHittingSpecification
universe u
theorem dimension_eq (n s : ℕ) : dimension n s = NCHitting.dimension n s := rfl
theorem expectedEntry_eq (n s : ℕ) : expectedEntry n s = NCHitting.generator n s := rfl
theorem expectedProgram_eq : expectedProgram = NCHitting.generatorProgram := rfl
theorem execute_expectedProgram_eq (n s : ℕ) :
NCHitting.BitModel.execute expectedProgram [n, s] = NCHitting.generate n s := rfl
theorem expectedOutput_eq (n s : ℕ) : expectedOutput n s = NCHitting.encodedOutput n s := rfl
theorem decode_eq : decode = NCHitting.decode := rfl
theorem entryBitBound_eq (n d : ℕ) : entryBitBound n d = NCHitting.entryBitBound n d := rfl
theorem costBound_eq (n s : ℕ) : costBound n s = NCHitting.generatorCostBound n s := rfl
theorem primitiveBitBound_eq (n s : ℕ) :
primitiveBitBound n s = NCHitting.primitiveBitBound n s := rfl
theorem completeClaim_of_hitting {n s : ℕ} (hn : 1 ≤ n) (hs : 1 ≤ s)
(hitting : UniversalHitting.{u} n s (dimension n s) (expectedEntry n s)) :
CompleteClaim.{u} n s := by
refine ⟨NCHitting.dimension_pos hn hs, NCHitting.dimension_le hn hs, ?_, ?_, ?_, ?_, ?_,
?_, hitting⟩
· exact NCHitting.generate_output n s
· exact NCHitting.generate_output_length n s
· exact NCHitting.generate_entry_bounds
· exact NCHitting.generate_entry_decode n s
· exact NCHitting.generate_cost_le n s
· exact NCHitting.generate_primitive_bit_bound n s
end NCHittingSpecification
end OAI
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