Theorems · Theorem · functional analysis
div_ball
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (s : Set E) (x : E),
s / Metric.ball x δ = x⁻¹ • Metric.thickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Metric.ballstatement and proof · cited by 735
- div_eq_mul_invproof · cited by 715
- Set.smulSetstatement · cited by 608
- SeminormedCommGroupstatement and proof · cited by 191
- Metric.thickeningstatement and proof · cited by 130
- Set.divstatement · cited by 112
- inv_ballproof · cited by 3
- mul_ballproof · cited by 2
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