instCompleteSpace — Mathlib

English

The function p ↦ mersenne(p) is strictly increasing on natural numbers.

Русский

Функция p ↦ mersenne(p) строго возрастает на натуральных числах.

LaTeX

$$$$\text{StrictMono}(\mathrm{mersenne})$$$$

Lean4

instance : CompleteSpace K :=
  letI : (Valued.v (R := K)).RankOne := ⟨IsRankLeOne.nonempty.some.emb, IsRankLeOne.nonempty.some.strictMono⟩
  open scoped Valued in
    have : ProperSpace K := .of_nontriviallyNormedField_of_weaklyLocallyCompactSpace K
    (properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField.mp inferInstance).1

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