le_minSmoothness — Mathlib

English

The function minSmoothness 𝕜 is monotone with respect to its second argument: if m ≤ n then minSmoothness 𝕜 m ≤ minSmoothness 𝕜 n.

Русский

Функция minSmoothness 𝕜 монотонна по второму аргументу: если m ≤ n, то minSmoothness 𝕜 m ≤ minSmoothness 𝕜 n.

LaTeX

$$$$ n \\leq \\minSmoothness_{\\mathbb{k}}(n) \\quad \\text{(monotone)} $$$$

Lean4

theorem le_minSmoothness {n : WithTop ℕ∞} : n ≤ minSmoothness 𝕜 n :=
  by
  simp only [minSmoothness]
  split_ifs <;> simp

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