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Theorems · Theorem · convex and discrete geometry

isExtreme_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] {A : Set E} {F : Set (Set E)}, F.Nonempty → (∀ B ∈ F, IsExtreme 𝕜 A B) → IsExtreme 𝕜 A (⋂₀ F)
Defined in
Mathlib.Analysis.Convex.Extreme
Cited by
1 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderAddCommMonoidSMul
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Around this declaration

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

IsCompact.extremePoints_nonempty · cited by 2IsCompact.extremePoints_n…Set · cited by 53352SetSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.Nonempty · cited by 2627Set.NonemptySet.sInter · cited by 225Set.sInterSet.sInter_eq_biInter · cited by 23Set.sInter_eq_biInterIsExtreme · cited by 22IsExtremeisExtreme_biInter · cited by 1isExtreme_biInterisExtreme_sInterCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.