Theorems · Theorem · functional analysis
sphere_zero_sub_singleton
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (x : E), Metric.sphere 0 δ - {x} = Metric.sphere (-x) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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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
- Metric.spherestatement and proof · cited by 371
- zero_subproof · cited by 335
- Set.substatement · cited by 136
- sphere_sub_singletonproof · cited by 4
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