Theorems · Theorem · functional analysis
balanced_iInter
∀ {𝕜 : Type u_1} {E : Type u_3} {ι : Sort u_5} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] {f : ι → Set E},
(∀ (i : ι), Balanced 𝕜 (f i)) → Balanced 𝕜 (⋂ i, f i)- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Norm.normproof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Set.iInterstatement · cited by 1,084
- SeminormedRingstatement and proof · cited by 446
- Balancedstatement and proof · cited by 77
- Set.iInter_monoproof · cited by 7
- Set.smul_set_iInter_subsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- balanced_iInter₂proof · cited by 1