to_rightInverse — Mathlib

English

If f is AntilipschitzWith K, and g is a RightInverse of f on t, then g is Lipschitz with constant K.

Русский

Если f антилипшицево с константой K и g — правая обратная на t, то g Lipschitz с константой K.

LaTeX

$$$AntilipschitzWith(K, f) \\Rightarrow ∀ g, RightInvOn g f t \\Rightarrow LipschitzWith(K, g)$$$

Lean4

theorem to_rightInverse (hf : AntilipschitzWith K f) {g : β → α} (hg : Function.RightInverse g f) : LipschitzWith K g :=
  by
  intro x y
  have := hf (g x) (g y)
  rwa [hg x, hg y] at this

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