Theorems · Theorem · functional analysis
Balanced.balancedHull_subset_of_subset
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] {s t : Set E},
Balanced 𝕜 t → s ⊆ t → balancedHull 𝕜 s ⊆ tThe balanced hull of s is minimal in the sense that it is contained in any balanced superset
t of s.
- Cited by
- 3 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.
Cites7
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
- Norm.normproof · cited by 5,413
- SeminormedRingstatement and proof · cited by 446
- Balancedstatement and proof · cited by 77
- balancedHullstatement and proof · cited by 12
- Balanced.smul_memproof · cited by 7
- mem_balancedHull_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- absConvexHull_eq_convexHull_balancedHullproof · cited by 2
- balancedHull_convexHull_subset_absConvexHullproof · cited by 1
- balancedHull_add_subsetproof · cited by 0