Theorems · Theorem · functional analysis
singleton_add_ball
∀ {E : Type u_1} [inst : SeminormedAddCommGroup 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
- 4 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- add_commproof · cited by 1,535
- Metric.ballstatement and proof · cited by 735
- Set.addstatement · cited by 338
- sub_neg_eq_addproof · cited by 264
- Set.image_add_leftproof · cited by 44
- Set.singleton_addproof · cited by 23
- preimage_add_ballproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- add_ball_zeroproof · cited by 4
- ball_add_singletonproof · cited by 1
- singleton_sub_ballproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1