Theorems · Theorem · functional analysis
closedBall_div_singleton
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (x y : E),
Metric.closedBall x δ / {y} = Metric.closedBall (x / y) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 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
- Set.inv_singletonproof · cited by 9
- closedBall_mul_singletonproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- closedBall_one_div_singletonproof · cited by 0