Theorems · Theorem · general topology

PairReduction.card_finset_logSizeBallSeq_add_one_lt

∀ {T : Type u_1} [inst : PseudoEMetricSpace T] {a c : ENNReal} {J : Finset T} [inst_1 : DecidableEq T] (hJ : J.Nonempty)
  (i : ℕ),
  (PairReduction.logSizeBallSeq J hJ a c i).finset.Nonempty →
    (PairReduction.logSizeBallSeq J hJ a c (i + 1)).finset.card < (PairReduction.logSizeBallSeq J hJ a c i).finset.card

Defined in: Mathlib.Topology.EMetricSpace.PairReduction
Cited by: 1 results in Mathlib
Foundations: Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoEMetricSpace DecidableEq

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Finsetstatement and proof · cited by 13,712
ENNRealstatement and proof · cited by 9,879
Finset.cardstatement · cited by 2,327
PseudoEMetricSpacestatement and proof · cited by 1,536
Finset.Nonemptystatement and proof · cited by 1,001
PairReduction.logSizeBallSeqstatement and proof · cited by 26
PairReduction.logSizeBallStruct.finsetstatement and proof · cited by 22
PairReduction.finset_logSizeBallSeq_add_one_ssubsetproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

PairReduction.card_finset_logSizeBallSeq_leproof · cited by 2