Theorems · Theorem · general topology
Nat.closedBall_eq_Icc
∀ (x : ℕ) (r : ℝ), Metric.closedBall x r = Set.Icc ⌈↑x - r⌉₊ ⌊↑x + r⌋₊
- Defined in
- Mathlib.Topology.Instances.Nat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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.preimageproof · cited by 4,946
- Nat.cast_zeroproof · cited by 1,870
- Set.Iccstatement and proof · cited by 1,702
- Metric.closedBallstatement · cited by 704
- le_of_not_gtproof · cited by 430
- lt_of_not_geproof · cited by 374
- le_or_gtproof · cited by 269
- Nat.cast_nonneg'proof · cited by 245
- Nat.floorstatement and proof · cited by 215
- Nat.ceilstatement and proof · cited by 141
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