connected_bot_iff — Mathlib

English

The bottom graph is connected iff V is a subsingleton and nonempty.

Русский

Нижний граф связан тогда, когда V — подслучайный и непустой.

LaTeX

$$$ (\perp : \mathrm{SimpleGraph}(V)).Connected \iff (\mathrm{Subsingleton}(V) \wedge \mathrm{Nonempty}(V)) $$$

Lean4

theorem connected_bot_iff : (⊥ : SimpleGraph V).Connected ↔ Subsingleton V ∧ Nonempty V := by
  simp [preconnected_bot_iff_subsingleton, connected_iff]

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