minSmoothness_eq_infty — Mathlib

English

minSmoothness 𝕜 n equals ∞ if and only if n = ∞ and the field is IsRCLikeNormedField.

Русский

minSmoothness 𝕜 n равно ∞ тогда, когда n = ∞ и поле является IsRCLikeNormedField.

LaTeX

$$$$ \\minSmoothness_{\\mathbb{k}}(n) = \\infty \\iff (n = \\infty \\land IsRCLikeNormedField 𝕜). $$$$

Lean4

@[simp]
theorem minSmoothness_eq_infty {n : WithTop ℕ∞} : minSmoothness 𝕜 n = ∞ ↔ (n = ∞ ∧ IsRCLikeNormedField 𝕜) :=
  by
  simp only [minSmoothness]
  split_ifs with h <;> simp [h]

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