absConvexHull_nonempty — Mathlib

English

absConvexHull 𝕜 s is nonempty if and only if s is nonempty.

Русский

absConvexHull 𝕜 s ненулевающе тогда, когда s ненулево.

LaTeX

$$$$ (\\operatorname{absConvexHull}_{\\mathbb{k}}(s)).\\text{Nonempty} \\iff s.\\text{Nonempty}. $$$$

Lean4

@[simp]
theorem absConvexHull_nonempty : (absConvexHull 𝕜 s).Nonempty ↔ s.Nonempty :=
  by
  rw [nonempty_iff_ne_empty, nonempty_iff_ne_empty, Ne, Ne]
  exact not_congr absConvexHull_eq_empty

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