Theorems · Theorem · general topology
Real.Icc_eq_closedBall
∀ (x y : ℝ), Set.Icc x y = Metric.closedBall ((x + y) / 2) ((y - x) / 2)
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Iccstatement and proof · cited by 1,702
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- Metric.closedBallstatement · cited by 704
- add_sub_cancel_leftproof · cited by 198
- add_sub_cancelproof · cited by 195
- add_divproof · cited by 89
- sub_addproof · cited by 51
- sub_divproof · cited by 37
- add_self_div_twoproof · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- Real.Icc_mem_vitaliFamily_at_leftproof · cited by 1
- Real.singleton_eq_inter_Iccproof · cited by 1
- Real.Icc_mem_vitaliFamily_at_rightproof · cited by 1
- Set.extremePoints_Iccproof · cited by 0
- unitInterval.eq_closedBallproof · cited by 0