dist_lineMap_lineMap — Mathlib

English

The trailing coefficient of f^n equals the nth power of the trailing coefficient of f for any integer n.

Русский

Хвостовой коэффициент f^n равен n-й степени хвостового коэффициента f для целого n.

LaTeX

$$$$ \mathrm{meromorphicTrailingCoeffAt}(f^n, x) = (\mathrm{meromorphicTrailingCoeffAt}(f, x))^{n}. $$$$

Lean4

@[simp]
theorem dist_lineMap_lineMap (p₁ p₂ : P) (c₁ c₂ : 𝕜) :
    dist (lineMap p₁ p₂ c₁) (lineMap p₁ p₂ c₂) = dist c₁ c₂ * dist p₁ p₂ :=
  by
  rw [dist_comm p₁ p₂]
  simp only [lineMap_apply, dist_eq_norm_vsub, vadd_vsub_vadd_cancel_right, ← sub_smul, norm_smul, vsub_eq_sub]

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