English
The embedding map is a contraction: dist(embeddingOfSubset x a, embeddingOfSubset x b) ≤ dist a b.
Русский
Отображение вложения является сжатием: dist(embeddingOfSubset x a, embeddingOfSubset x b) ≤ dist(a,b).
LaTeX
$$$\operatorname{dist}(\mathrm{embeddingOfSubset}(x,a), \mathrm{embeddingOfSubset}(x,b)) \le \operatorname{dist}(a,b)$$$
Lean4
protected theorem mk_one (h : ∀ x y, dist (f x) (f y) ≤ dist x y) : LipschitzWith 1 f :=
of_dist_le_mul <| by simpa only [NNReal.coe_one, one_mul] using h