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Theorems · Theorem · functional analysis

mem_balancedCore_iff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] {s : Set E} {x : E},
  x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ x ∈ t
Defined in
Mathlib.Analysis.LocallyConvex.BalancedCoreHull
Cited by
2 results in Mathlib
Foundations
Depth 97 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.

balancedCore_zero_mem · cited by 2balancedCore_zero_memsmul_balancedCore_subset · cited by 1smul_balancedCore_subsetSet · cited by 53352SetSeminormedRing · cited by 446SeminormedRingBalanced · cited by 77BalancedbalancedCore · cited by 18balancedCoremem_balancedCore_iffCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.