Theorems · Theorem · general topology
PairReduction.exists_radius_le
∀ {T : Type u_1} [inst : PseudoEMetricSpace T] {a : ENNReal} (t : T) (V : Finset T),
1 < a → ∀ (c : ENNReal), ∃ r, 1 ≤ r ∧ ↑{x ∈ V | edist t x ≤ ↑r * c}.card ≤ a ^ r- Cited by
- 4 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Filter.Eventuallyproof · cited by 3,134
- Filter.atTopproof · cited by 2,405
- Finset.cardstatement and proof · cited by 2,327
- LT.lt.leproof · cited by 2,189
- PseudoEMetricSpacestatement and proof · cited by 1,536
- le_transproof · cited by 985
- Finset.filterstatement · cited by 949
- EDist.ediststatement and proof · cited by 735
- Filter.Tendsto.compproof · cited by 560
Cited by5
Results whose statement or proof uses this declaration.
- PairReduction.logSizeRadiusproof · cited by 7
- PairReduction.card_le_logSizeRadius_le_pow_logSizeRadiusproof · cited by 1
- PairReduction.one_le_logSizeRadiusproof · cited by 1
- PairReduction.pow_logSizeRadius_le_card_le_logSizeRadiusproof · cited by 1
- PairReduction.radius_logSizeBallSeq_leproof · cited by 1