Theorems · Theorem · functional analysis

NormedSpace.sphere_nonempty_rclike

∀ (𝕜 : Type u_1) [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [NormedSpace 𝕜 E] [Nontrivial E]
  {r : ℝ}, 0 ≤ r → Nonempty ↑(Metric.sphere 0 r)

Defined in: Mathlib.Analysis.Normed.Module.RCLike.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup NormedSpace Nontrivial

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Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
Set.Elemstatement · cited by 7,166
RCLikestatement and proof · cited by 2,829
Nontrivialstatement and proof · cited by 2,416
Metric.spherestatement · cited by 371
NormedSpace.sphere_nonemptyproof · cited by 8
Set.Nonempty.coe_sortproof · cited by 6

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