Theorems · Theorem · functional analysis
closedBall_sub_singleton
∀ {E : Type u_1} [inst : SeminormedAddCommGroup 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
- 4 results in Mathlib
- Foundations
- Depth 164 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.
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- sub_eq_add_negproof · cited by 1,023
- Metric.closedBallstatement and proof · cited by 704
- Set.substatement · cited by 136
- Set.neg_singletonproof · cited by 14
- closedBall_add_singletonproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- meromorphicNFOn_closedBall_comp_sub_const_iff_meromorphicNFOn_closedBallproof · cited by 1
- MeromorphicOn.divisor_closedBall_comp_sub_const_eq_divisor_closedBallproof · cited by 1
- closedBall_zero_sub_singletonproof · cited by 0