Theorems · Theorem · general topology
Real.closedBall_eq_Icc
∀ {x r : ℝ}, Metric.closedBall x r = Set.Icc (x - r) (x + r)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.extproof · cited by 2,266
- Set.Iccstatement and proof · cited by 1,702
- Metric.closedBallstatement · cited by 704
- dist_commproof · cited by 188
- Set.mem_Iccproof · cited by 46
- Metric.mem_closedBallproof · cited by 42
- sub_le_iff_le_add'proof · cited by 41
- abs_sub_le_iffproof · cited by 34
- Real.dist_eqproof · cited by 27
- sub_le_commproof · cited by 19
Cited by13
Results whose statement or proof uses this declaration.
- Real.Icc_eq_closedBallproof · cited by 6
- Real.volume_closedBallproof · cited by 5
- AddCircle.volume_closedBallproof · cited by 4
- PhragmenLindelof.horizontal_stripproof · cited by 3
- Real.tendsto_Icc_vitaliFamily_leftproof · cited by 2
- Real.tendsto_Icc_vitaliFamily_rightproof · cited by 2
- AddCircle.coe_real_preimage_closedBall_inter_eqproof · cited by 1
- isBigO_norm_restrict_cocompactproof · cited by 1
- Liouville.exists_pos_real_of_irrational_rootproof · cited by 1
- Int.closedBall_eq_Iccproof · cited by 0
- Nat.closedBall_eq_Iccproof · cited by 0
- Real.closedBall_eq_segmentproof · cited by 0