Theorems · Theorem · general topology

PairReduction.logSizeRadius_le_card_smallBall

∀ {T : Type u_1} [inst : PseudoEMetricSpace T] {a c : ENNReal} {J : Finset T} [inst_1 : DecidableEq T] (hJ : J.Nonempty)
  (i : ℕ),
  1 < a →
    (if (PairReduction.logSizeBallSeq J hJ a c i).finset.Nonempty then 1 else 0) *
        a ^ ((PairReduction.logSizeBallSeq J hJ a c i).radius - 1) ≤
      ↑((PairReduction.logSizeBallSeq J hJ a c i).smallBall c).card

Defined in

Mathlib.Topology.EMetricSpace.PairReduction

Cited by

1 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpaceDecidableEq