| 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 |
|
|
