Theorems · Theorem · functional analysis
sphere_sub_singleton
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (x y : E), Metric.sphere x δ - {y} = Metric.sphere (x - y) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- sub_eq_add_negproof · cited by 1,023
- Metric.spherestatement and proof · cited by 371
- Set.substatement · cited by 136
- Set.neg_singletonproof · cited by 14
- sphere_add_singletonproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- MeromorphicOn.divisor_sphere_comp_sub_const_eq_divisor_sphereproof · cited by 1
- meromorphicNFOn_sphere_comp_sub_const_iff_meromorphicNFOn_sphereproof · cited by 1
- sphere_zero_sub_singletonproof · cited by 0