Theorems · Theorem · functional analysis
balancedCore_eq_iInter
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set E}, 0 ∈ s → balancedCore 𝕜 s = ⋂ r, ⋂ (_ : 1 ≤ ‖r‖), r • s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement · cited by 5,413
- Set.iInterstatement · cited by 1,084
- Set.smulSetstatement · cited by 608
- LE.le.antisymmproof · cited by 507
- NormedDivisionRingstatement and proof · cited by 360
- balancedCorestatement · cited by 18
- balancedCore_zero_memproof · cited by 2
- Balanced.subset_balancedCore_of_subsetproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- subset_balancedCoreproof · cited by 1
- IsClosed.balancedCoreproof · cited by 1