Theorems · Theorem · general topology
dist_le_zero
∀ {γ : Type w} [inst : MetricSpace γ] {x y : γ}, dist x y ≤ 0 ↔ x = y- Defined in
- Mathlib.Topology.MetricSpace.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 113 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 and proof · cited by 1,539
- dist_eq_zeroproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- norm_le_zero_iffproof · cited by 23
- Metric.closedBall_zeroproof · cited by 13
- dist_posproof · cited by 12
- ODE_solution_unique_of_mem_Icc_rightproof · cited by 4
- norm_le_zero_iff'proof · cited by 3
- exists_nat_nat_continuous_surjective_of_completeSpaceproof · cited by 1
- IsometryEquiv.midpoint_fixedproof · cited by 1