Theorems · Theorem · functional analysis
Balanced.subset_smul
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set E} {a : 𝕜}, Balanced 𝕜 s → 1 ≤ ‖a‖ → s ⊆ a • s- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement and proof · cited by 5,413
- one_smulproof · cited by 1,374
- Set.smulSetstatement · cited by 608
- NormedDivisionRingstatement and proof · cited by 360
- NormOneClass.norm_oneproof · cited by 148
- Balancedstatement and proof · cited by 77
- Balanced.smul_monoproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Balanced.absorbs_selfproof · cited by 1
- Balanced.smul_eqproof · cited by 0