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Theorems · Theorem · functional analysis

Balanced.sInter

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] {S : Set (Set E)},
  (∀ s ∈ S, Balanced 𝕜 s) → Balanced 𝕜 (⋂₀ S)
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
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AbsConvex.sInter · cited by 3AbsConvex.sInterSet · cited by 53352SetNorm.norm · cited by 5413Norm.normLE.le.trans · cited by 3151le.transSet.iInter · cited by 1084Set.iInterSeminormedRing · cited by 446SeminormedRingSet.sInter · cited by 225Set.sInterBalanced · cited by 77BalancedSet.smul_set_sInter_subset · cited by 1Set.smul_set_sInter_subsetBalanced.sInterCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.