weaken — Mathlib

English

If h maps s into t, then LipschitzOnWith K f s is equivalent to LipschitzWith K (Set.MapsTo.restrict f s t).

Русский

Если h отображает s в t, то LipOnWith K f s эквивалентен LipWith K (Set.MapsTo.restrict f s t).

LaTeX

$$$MapsTo\ f\ s\ t\Rightarrow (LipschitzOnWith K f s\iff LipschitzWith K (Set.MapsTo.restrict f s t))$$$

Lean4

protected theorem weaken (hf : LipschitzWith K f) {K' : ℝ≥0} (h : K ≤ K') : LipschitzWith K' f := fun x y =>
  le_trans (hf x y) <| mul_left_mono (ENNReal.coe_le_coe.2 h)

Похожие утверждения