Theorems · Theorem · general topology
Set.infsep_pair_eq_toReal
∀ {α : Type u_1} [inst : PseudoEMetricSpace α] {x y : α}, {x, y}.infsep = (edist x y).toReal- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 148 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealproof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.toRealstatement and proof · cited by 859
- EDist.ediststatement and proof · cited by 735
- PseudoEMetricSpace.edist_selfproof · cited by 50
- Set.infsepstatement and proof · cited by 35
- Set.pair_eq_singletonproof · cited by 3
- Set.infsep_singletonproof · cited by 1
- Set.einfsep_pairproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Set.infsep_pairproof · cited by 0