Theorems · Theorem · general topology

PairReduction.finset_logSizeBallSeq_add_one_ssubset

∀ {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 ⊂ (PairReduction.logSizeBallSeq J hJ a c i).finset

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: PseudoEMetricSpace DecidableEq

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Cites11

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
PseudoEMetricSpacestatement and proof · cited by 1,536
Finset.Nonemptystatement and proof · cited by 1,001
Set.not_subsetproof · cited by 31
PairReduction.logSizeBallSeqstatement and proof · cited by 26
PairReduction.logSizeBallStruct.finsetstatement and proof · cited by 22
PairReduction.logSizeBallStruct.pointproof · cited by 15
PairReduction.point_mem_finset_logSizeBallSeqproof · cited by 3
PairReduction.point_notMem_finset_logSizeBallSeq_add_oneproof · cited by 1
ssubset_of_subset_not_subsetproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

PairReduction.card_finset_logSizeBallSeq_add_one_ltproof · cited by 1