nndist_center_homothety — Mathlib

English

The trailing coefficient of a scalar-times-vector product equals the scalar times the trailing coefficient of the vector function.

Русский

Хвостовой коэффициент скалярного произведения равен произведению скаляра на хвостовой коэффициент вектора.

LaTeX

$$$$ \mathrm{meromorphicTrailingCoeffAt}(\lambda z. f(z) \cdot g(z), x) = (\mathrm{meromorphicTrailingCoeffAt}(\lambda z. f(z), x)) \cdot (\mathrm{meromorphicTrailingCoeffAt}(g, x)). $$$$

Lean4

@[simp]
theorem nndist_center_homothety (p₁ p₂ : P) (c : 𝕜) : nndist p₁ (homothety p₁ c p₂) = ‖c‖₊ * nndist p₁ p₂ :=
  NNReal.eq <| dist_center_homothety _ _ _

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