Theorems · Theorem · functional analysis
singleton_mul_sphere
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (x y : E), {x} * Metric.sphere y δ = Metric.sphere (x * y) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.image_congrproof · cited by 533
- Metric.spherestatement and proof · cited by 371
- Set.mulstatement · cited by 297
- SeminormedCommGroupstatement and proof · cited by 191
- Set.singleton_mulproof · cited by 9
- Metric.smul_sphereproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- sphere_mul_singletonproof · cited by 2
- singleton_div_sphereproof · cited by 1
- singleton_mul_sphere_oneproof · cited by 0