mul_le_edist — Mathlib

English

The pullback of the uniformity on β along (f,f) is below the uniformity on α.

Русский

Обратная связь униформности β по (f,f) меньше униформности α.

LaTeX

$$$(\\mathcal{U}\\beta).comap (Prod.map\) f f \\le \\mathcal{U}\\alpha$$$

Lean4

theorem mul_le_edist (hf : AntilipschitzWith K f) (x y : α) : (K : ℝ≥0∞)⁻¹ * edist x y ≤ edist (f x) (f y) :=
  by
  rw [mul_comm, ← div_eq_mul_inv]
  exact ENNReal.div_le_of_le_mul' (hf x y)

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