Theorems · Theorem · functional analysis
singleton_mul_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
- 3 results in Mathlib
- Foundations
- Depth 94 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.
Cites10
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
- mul_commproof · cited by 2,262
- Metric.ballstatement and proof · cited by 735
- Set.mulstatement · cited by 297
- SeminormedCommGroupstatement and proof · cited by 191
- div_inv_eq_mulproof · cited by 53
- Set.image_mul_leftproof · cited by 21
- Set.singleton_mulproof · cited by 9
- preimage_mul_ballproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- mul_ball_oneproof · cited by 3
- singleton_div_ballproof · cited by 1
- ball_mul_singletonproof · cited by 1