List Block subset list Hamming
BlockRelDistance.listBlock_subset_listHamming
Plain-language statement
Claim 4.19 from [ACFY24], Part 2 As a consequence of relHammingDist_le_blockRelDistance, the list of codewords within a certain block relative distance δ is a subset of the list of codewords within the same relative Hamming distance δ.
Exact Lean statement
lemma listBlock_subset_listHamming (hkn : k ≤ n) (δ : ℝ≥0) (C : Set (Fin (2 ^ n) → F)) : Λ𞁒(C, k, φ, f, δ) ⊆ closeCodewordsRel C f δ
Formal artifact
Lean source
lemma listBlock_subset_listHamming (hkn : k ≤ n) (δ : ℝ≥0) (C : Set (Fin (2 ^ n) → F)) : Λ𞁒(C, k, φ, f, δ) ⊆ closeCodewordsRel C f δ := by intro u hu simp only [blockRelDistanceBall, Set.mem_sep_iff] at hu refine ⟨hu.1, ?_⟩ have h1 := relHammingDist_le_blockRelDistance (φ := φ) (k := k) (f := f) (g := u) hkn simp only [relHammingBall, Set.mem_setOf_eq, ge_iff_le] apply le_trans (b := NNRat.cast δ𞁒(k, φ, f, u)) · rewrite [NNRat.cast_le] convert h1 · aesop- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/Data/CodingTheory/Basic/BlockRelDistance.lean:284-296
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Person-level attribution pending.
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Plain-language statement
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Source project: ArkLib
Person-level attribution pending.