Theorems · Theorem · functional analysis
singleton_div_closedBall
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (x y : E),
{x} / Metric.closedBall y δ = Metric.closedBall (x / y) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 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
- div_eq_mul_invproof · cited by 715
- Metric.closedBallstatement and proof · cited by 704
- SeminormedCommGroupstatement and proof · cited by 191
- Set.divstatement · cited by 112
- inv_closedBallproof · cited by 3
- singleton_mul_closedBallproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- singleton_div_closedBall_oneproof · cited by 0