Theorems · Theorem · functional analysis
mem_sphere_one_iff_norm
∀ {E : Type u_5} [inst : SeminormedGroup E] {a : E} {r : ℝ}, a ∈ Metric.sphere 1 r ↔ ‖a‖ = r- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Norm.normstatement and proof · cited by 5,413
- Metric.spherestatement · cited by 371
- SeminormedGroupstatement and proof · cited by 250
- dist_one_rightproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- norm_eq_of_mem_sphere'proof · cited by 1