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Theorems · Theorem · convex and discrete geometry

starConvex_sInter

∀ {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} {S : Set (Set E)}, (∀ s ∈ S, StarConvex 𝕜 x s) → StarConvex 𝕜 x (⋂₀ S)
Defined in
Mathlib.Analysis.Convex.Star
Cited by
3 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
SemiringPartialOrderAddCommMonoidSMul
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Around this declaration

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

convex_sInter · cited by 2convex_sInterstarConvex_iInter · cited by 1starConvex_iInterconvex_closed_sInter · cited by 0convex_closed_sInterSet · cited by 53352SetSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.sInter · cited by 225Set.sInterStarConvex · cited by 62StarConvexstarConvex_sInterCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.