denseRange_cast — Mathlib

English

There is a canonical coercion from OpenNormalSubgroup G to Subgroup G given by H ↦ H.toOpenSubgroup.toSubgroup.

Русский

Существует каноническое приведение OpenNormalSubgroup G к Subgroup G через H ↦ H.toOpenSubgroup.toSubgroup.

LaTeX

$$coe : OpenNormalSubgroup(G) → Subgroup(G) with coe(H) = H.toOpenSubgroup.toSubgroup$$

Lean4

/-- Rational numbers are dense in a linear ordered archimedean field. -/
theorem denseRange_cast {𝕜} [Field 𝕜] [LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [TopologicalSpace 𝕜] [OrderTopology 𝕜]
    [Archimedean 𝕜] : DenseRange ((↑) : ℚ → 𝕜) :=
  dense_of_exists_between fun _ _ h => Set.exists_range_iff.2 <| exists_rat_btwn h

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