cutMap_bddAbove — Mathlib

English

For finite s and function f, the mean of squares dominates the mean of the values: (∑ f(i)^2)/|s| ≥ ( (∑ f(i))/|s| )^2.

Русский

Для конечного s и функции f среднее по квадратам не меньше квадрата среднего значения: (∑ f(i)^2)/|s| ≥ ( (∑ f(i))/|s| )^2.

LaTeX

$$$\frac{\sum_{i \in s} f(i)^2}{|s|} \ge \left(\frac{\sum_{i \in s} f(i)}{|s|}\right)^2$$$

Lean4

theorem cutMap_bddAbove (a : α) : BddAbove (cutMap β a) :=
  by
  obtain ⟨q, hq⟩ := exists_rat_gt a
  exact ⟨q, forall_mem_image.2 fun r hr => mod_cast (hq.trans' hr).le⟩

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