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Theorems · Theorem · convex and discrete geometry

Set.Nonempty.convexHull

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : Module 𝕜 E] {s : Set E}, s.Nonempty → ((convexHull 𝕜) s).Nonempty

Alias of the reverse direction of convexHull_nonempty_iff.

Defined in
Mathlib.Analysis.Convex.Hull
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderAddCommMonoidModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

convexHull_union · cited by 1convexHull_unionDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.Nonempty · cited by 2627Set.NonemptyClosureOperator · cited by 371ClosureOperatorconvexHull · cited by 163convexHullconvexHull_nonempty_iff · cited by 6convexHull_nonempty_iffNonempty.convexHullCITED BYCITES

Cites10

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Cited by1

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