Theorems · Theorem · general topology
Set.einfsep_pos_of_finite
∀ {α : Type u_1} [inst : EMetricSpace α] {s : Set α} [Finite ↑s], 0 < s.einfsep- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpaceFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- EDist.edistproof · cited by 735
- nonempty_fintypeproof · cited by 261
- EMetricSpacestatement and proof · cited by 242
- Set.Nontrivialproof · cited by 145
- Set.einfsepstatement and proof · cited by 47
- Set.not_nontrivial_iffproof · cited by 13
- WithTop.top_posproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Set.infsep_zero_iff_subsingleton_of_finiteproof · cited by 2
- Set.infsep_pos_iff_nontrivial_of_finiteproof · cited by 2
- Set.relatively_discrete_of_finiteproof · cited by 1
- Set.Finite.einfsep_posproof · cited by 0