Theorems · Theorem · functional analysis
singleton_div_ball
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (x y : E), {x} / Metric.ball y δ = Metric.ball (x / y) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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
- Metric.ballstatement and proof · cited by 735
- div_eq_mul_invproof · cited by 715
- SeminormedCommGroupstatement and proof · cited by 191
- Set.divstatement · cited by 112
- inv_ballproof · cited by 3
- singleton_mul_ballproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- singleton_div_ball_oneproof · cited by 0