Theorems · Theorem · functional analysis
smul_balancedCore_subset
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] (s : Set E) {a : 𝕜},
‖a‖ ≤ 1 → a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 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.
Cites9
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 · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Set.smulSetstatement · cited by 608
- SeminormedRingstatement and proof · cited by 446
- Balancedproof · cited by 77
- Set.smul_mem_smul_setproof · cited by 39
- balancedCorestatement and proof · cited by 18
- mem_balancedCore_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- balancedCore_balancedproof · cited by 6