Theorems · Theorem · functional analysis
Balanced.neg_mem_iff
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {s : Set E}
[NormOneClass 𝕜], Balanced 𝕜 s → ∀ {x : E}, -x ∈ s ↔ x ∈ s- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- one_smulproof · cited by 1,374
- neg_negproof · cited by 960
- SeminormedRingstatement and proof · cited by 446
- neg_smulproof · cited by 306
- norm_negproof · cited by 190
- smul_negproof · cited by 181
- NormOneClass.norm_oneproof · cited by 148
- NormOneClassstatement and proof · cited by 136
- Balancedstatement and proof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- balanced_iff_neg_memproof · cited by 0
- Balanced.neg_eqproof · cited by 0