Theorems · Theorem · functional analysis
AbsConvex.iInter
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] [inst_2 : AddCommMonoid E]
[inst_3 : PartialOrder 𝕜] {ι : Sort u_3} {s : ι → Set E}, (∀ (i : ι), AbsConvex 𝕜 (s i)) → AbsConvex 𝕜 (⋂ i, s i)- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Set.iInterstatement · cited by 1,084
- SeminormedRingstatement and proof · cited by 446
- Set.forall_mem_rangeproof · cited by 135
- AbsConvexstatement and proof · cited by 31
- Set.sInter_rangeproof · cited by 16
- AbsConvex.sInterproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AbsConvex.iInter₂proof · cited by 1