of_dist_le' — Mathlib

English

The embeddingOfSubset_coe gives the coordinate value of embeddingOfSubset.

Русский

embeddingOfSubset_coe задаёт координатное значение embeddingOfSubset.

LaTeX

$$$\mathrm{embeddingOfSubset}_{n}(x,a) = \operatorname{dist}(a, x_n) - \operatorname{dist}(x_0, x_n)$$$

Lean4

protected theorem of_dist_le' {K : ℝ} (h : ∀ x y, dist (f x) (f y) ≤ K * dist x y) :
    LipschitzWith (Real.toNNReal K) f :=
  of_dist_le_mul fun x y => le_trans (h x y) <| by gcongr; apply Real.le_coe_toNNReal

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