of_nhds_neBot — Mathlib

English

If the meet (infimum) of nhds x and nhds y is nontrivial (NeBot), then x and y are inseparable.

Русский

Если нижний предел обзоров nhds x и nhds y не пустой, то x и y несепризмны (inseparable).

LaTeX

$$$ (\\nhds x \\sqcap \\nhds y).NeBot \\Rightarrow Inseparable x y. $$$

Lean4

theorem of_nhds_neBot {x y : X} (h : NeBot (𝓝 x ⊓ 𝓝 y)) : Inseparable x y :=
  (r1Space_iff_inseparable_or_disjoint_nhds.mp ‹_› _ _).resolve_right fun h' => h.ne h'.eq_bot

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