Theorems · Theorem · general topology
Set.einfsep_pair_eq_inf
∀ {α : Type u_1} [inst : EDist α] {x y : α}, x ≠ y → {x, y}.einfsep = min (edist x y) (edist y x)- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EDist
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement · cited by 9,879
- le_antisymmproof · cited by 2,068
- EDist.ediststatement · cited by 735
- le_infproof · cited by 107
- EDiststatement and proof · cited by 91
- Set.einfsepstatement · cited by 47
- Set.einfsep_pair_le_leftproof · cited by 2
- Set.le_einfsep_pairproof · cited by 1
- Set.einfsep_pair_le_rightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.einfsep_pairproof · cited by 1
- Set.infsep_pair_le_toReal_infproof · cited by 0