Theorems · Theorem · general topology
zero_eq_dist
∀ {γ : Type w} [inst : MetricSpace γ] {x y : γ}, 0 = dist x y ↔ x = y- Defined in
- Mathlib.Topology.MetricSpace.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- dist_eq_zeroproof · cited by 13
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.