dist_right_lineMap — Mathlib

English

The trailing coefficient of the line map is linear in the parameter with the coefficient equal to the line map coefficient.

Русский

Хвостовой коэффициент линейной карты пропорционален параметру и равен коэффициенту линейной карты.

LaTeX

$$$$ \mathrm{meromorphicTrailingCoeffAt}(\text{lineMap}(-,-), x) = \text{lineMap coeff at } x. $$$$

Lean4

@[simp]
theorem dist_right_lineMap (p₁ p₂ : P) (c : 𝕜) : dist p₂ (lineMap p₁ p₂ c) = ‖1 - c‖ * dist p₁ p₂ :=
  (dist_comm _ _).trans (dist_lineMap_right _ _ _)

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