dist_homothety_center — Mathlib

English

The trailing coefficient of a product is the product of trailing coefficients.

Русский

Хвостовой коэффициент произведения равен произведению хвостовых коэффициентов.

LaTeX

$$$$ \mathrm{meromorphicTrailingCoeffAt}(f_1 \cdot f_2, x) = \mathrm{meromorphicTrailingCoeffAt}(f_1,x) \cdot \mathrm{meromorphicTrailingCoeffAt}(f_2,x). $$$$

Lean4

@[simp]
theorem dist_homothety_center (p₁ p₂ : P) (c : 𝕜) : dist (homothety p₁ c p₂) p₁ = ‖c‖ * dist p₁ p₂ := by
  rw [dist_comm, dist_center_homothety]

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