Theorems · Theorem · functional analysis
balancedCore_nonempty_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {s : Set E},
(balancedCore 𝕜 s).Nonempty ↔ 0 ∈ s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LE.le.transproof · cited by 3,151
- Set.Nonemptystatement and proof · cited by 2,627
- SeminormedRingstatement and proof · cited by 446
- norm_zeroproof · cited by 366
- zero_le_oneproof · cited by 316
- Eq.trans_leproof · cited by 155
- Set.zero_smul_setproof · cited by 20
- balancedCorestatement and proof · cited by 18
- Eq.supersetproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Balanced.zero_memproof · cited by 1
- IsClosed.balancedCoreproof · cited by 1