Theorems · Theorem · functional analysis
ball_sub_singleton
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (x y : E), Metric.ball x δ - {y} = Metric.ball (x - y) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 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.ballstatement and proof · cited by 735
- Set.substatement · cited by 136
- Set.neg_singletonproof · cited by 14
- ball_add_singletonproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- MeromorphicOn.divisor_ball_comp_sub_const_eq_divisor_ballproof · cited by 1
- MeromorphicOn.meromorphicOn_ball_comp_sub_const_iff_meromorphicOn_ballproof · cited by 1
- meromorphicNFOn_ball_comp_sub_const_iff_meromorphicNFOn_ballproof · cited by 1
- ball_zero_sub_singletonproof · cited by 0