Theorems · Theorem · general topology
edist_le_zero
∀ {γ : Type w} [inst : EMetricSpace γ] {x y : γ}, edist x y ≤ 0 ↔ x = y- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- EDist.ediststatement · cited by 735
- EMetricSpacestatement and proof · cited by 242
- nonpos_iff_eq_zeroproof · cited by 100
- edist_eq_zeroproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- ContractingWith.eq_or_edist_eq_top_of_fixedPointsproof · cited by 3
- AntilipschitzWith.subsingletonproof · cited by 2
- Metric.ediam_eq_zero_iffproof · cited by 1