nndist_lineMap_lineMap — Mathlib

English

The trailing coefficient of f^n with n ∈ ℕ equals the nth power of the trailing coefficient of f.

Русский

Хвостовой коэффициент f^n при n ∈ ℕ равен n-й степени хвостового коэффициента f.

LaTeX

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

Lean4

@[simp]
theorem nndist_lineMap_lineMap (p₁ p₂ : P) (c₁ c₂ : 𝕜) :
    nndist (lineMap p₁ p₂ c₁) (lineMap p₁ p₂ c₂) = nndist c₁ c₂ * nndist p₁ p₂ :=
  NNReal.eq <| dist_lineMap_lineMap _ _ _ _

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