specializes_comm — Mathlib

English

In an R0 space, Specializes is equivalent to Inseparable; i.e., Specializes x y iff Inseparable x y.

Русский

В пространстве R0 специализация эквивалентна inseparable; то есть Specializes x y ⇔ Inseparable x y.

LaTeX

$$$x \\mathrel{\\rhd} y \\iff Inseparable(x,y)$$$

Lean4

/-- In an R₀ space, the `Specializes` relation is symmetric, `Iff` version. -/
theorem specializes_comm : x ⤳ y ↔ y ⤳ x :=
  ⟨Specializes.symm, Specializes.symm⟩

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