minSmoothness_monotone — Mathlib

English

For any n, minSmoothness 𝕜 n is monotone with respect to the natural order, i.e., if m ≤ n then minSmoothness 𝕜 m ≤ minSmoothness 𝕜 n.

Русский

Для любого n мин Smoothness 𝕜 n монотонна по естественному порядку: если m ≤ n, то minSmoothness 𝕜 m ≤ minSmoothness 𝕜 n.

LaTeX

$$$$ m \\le n \\implies \\minSmoothness_{\\mathbb{k}}(m) \\le \\minSmoothness_{\\mathbb{k}}(n). $$$$

Lean4

theorem minSmoothness_monotone : Monotone (minSmoothness 𝕜) :=
  by
  intro m n hmn
  simp only [minSmoothness]
  split_ifs <;> simp [hmn]

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