Theorems · Theorem · functional analysis
norm_eq_of_mem_sphere
∀ {E : Type u_5} [inst : SeminormedAddGroup E] {r : ℝ} (x : ↑(Metric.sphere 0 r)), ‖↑x‖ = r- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- SeminormedAddGroup
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- Norm.normstatement · cited by 5,413
- Metric.spherestatement and proof · cited by 371
- SeminormedAddGroupstatement and proof · cited by 331
- mem_sphere_zero_iff_normproof · cited by 13
Cited by11
Results whose statement or proof uses this declaration.
- Circle.norm_smulproof · cited by 8
- ne_zero_of_mem_sphereproof · cited by 3
- Circle.normSq_coeproof · cited by 2
- ContMDiff.codRestrict_sphereproof · cited by 2
- stereographic_apply_negstatement and proof · cited by 1
- rotationOf_rotationproof · cited by 1
- stereo_left_invproof · cited by 0
- IsOpen.smul_sphereproof · cited by 0
- stereographic_neg_applystatement and proof · cited by 0
- sphere_ext_iffproof · cited by 0