Theorems · Theorem · convex and discrete geometry
isExtreme_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] {A : Set E} {ι : Sort u_6} [Nonempty ι] {F : ι → Set E},
(∀ (i : ι), IsExtreme 𝕜 A (F i)) → IsExtreme 𝕜 A (⋂ i, F i)- Defined in
- Mathlib.Analysis.Convex.Extreme
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Set.iInterstatement and proof · cited by 1,084
- openSegmentproof · cited by 102
- Set.mem_iInterproof · cited by 69
- IsExtremestatement and proof · cited by 22
- Set.iInter_subset_of_subsetproof · cited by 9
- IsExtreme.subsetproof · cited by 6
- IsExtreme.left_mem_of_mem_openSegmentproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- isExtreme_biInterproof · cited by 1