Theorems · Definition · general topology
PairReduction.pairSet
{T : Type u_1} → [PseudoEMetricSpace T] → [DecidableEq T] → Finset T → ENNReal → ENNReal → Finset (T × T)Given the pair set sequence Kᵢ we define the pair set K by K = ⋃ i, Kᵢ.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.cardproof · cited by 2,327
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Finset.rangeproof · cited by 1,341
- Finset.biUnionproof · cited by 217
- PairReduction.pairSetSeqproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- PairReduction.pairSet_subsetstatement · cited by 2
- PairReduction.card_pairSet_lestatement and proof · cited by 1
- PairReduction.edist_le_of_mem_pairSetstatement and proof · cited by 1
- PairReduction.iSup_edist_pairSetstatement and proof · cited by 1
- EMetric.pair_reductionproof · cited by 0
- PairReduction.pairSet_empty_eq_emptystatement · cited by 0