Theorems · Theorem · general topology
eq_of_forall_dist_le
∀ {γ : Type w} [inst : MetricSpace γ] {x y : γ}, (∀ ε > 0, dist x y ≤ ε) → x = y- Defined in
- Mathlib.Topology.MetricSpace.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- dist_nonnegproof · cited by 126
- eq_of_le_of_forall_lt_imp_le_of_denseproof · cited by 4
- eq_of_dist_eq_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- PadicInt.lift_uniqueproof · cited by 1