nnnorm_eq_hammingNorm — Mathlib

English

The proof that Hamming β inherits NormedAddGroup structure from its components is given by the compatibility of the distance with hammingNorm.

Русский

Доказательство переноса структуры NormedAddGroup на Hamming β следует из совместимости метрики с нормой Хэмминга.

LaTeX

$$Proof of NormedAddGroup structure on Hamming β$$

Lean4

@[simp, push_cast]
theorem nnnorm_eq_hammingNorm [∀ i, AddGroup (β i)] (x : Hamming β) : ‖x‖₊ = hammingNorm (ofHamming x) :=
  rfl

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