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Theorems · Theorem · convex and discrete geometry

starConvex_iInter

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : SMul 𝕜 E] {x : E} {ι : Sort u_4} {s : ι → Set E},
  (∀ (i : ι), StarConvex 𝕜 x (s i)) → StarConvex 𝕜 x (⋂ i, s i)
Defined in
Mathlib.Analysis.Convex.Star
Cited by
1 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
SemiringPartialOrderAddCommMonoidSMul
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Around this declaration

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

starConvex_iInter₂ · cited by 0starConvex_iInter₂Set · cited by 53352SetSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.iInter · cited by 1084Set.iInterSet.forall_mem_range · cited by 135Set.forall_mem_rangeStarConvex · cited by 62StarConvexSet.sInter_range · cited by 16Set.sInter_rangestarConvex_sInter · cited by 3starConvex_sInterstarConvex_iInterCITED BYCITES

Cites9

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Cited by1

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