norm_eq_hammingNorm — Mathlib

English

The inverse encoding respects subtraction: ofHamming (x - y) = ofHamming x - ofHamming y.

Русский

Обратное кодирование сохраняет вычитание: ofHamming (x - y) = ofHamming x - ofHamming y.

LaTeX

$$$\\operatorname{ofHamming}(x - y) = \\operatorname{ofHamming}(x) - \\operatorname{ofHamming}(y)$$$

Lean4

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

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