Theorems · Theorem · convex and discrete geometry
convex_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] {S : Set (Set E)}, (∀ s ∈ S, Convex 𝕜 s) → Convex 𝕜 (⋂₀ S)- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Convexstatement and proof · cited by 551
- Set.sInterstatement and proof · cited by 225
- starConvex_sInterproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AbsConvex.sInterproof · cited by 3
- convex_iInterproof · cited by 3