Theorems · Theorem · general topology
Metric.infEDist_le_infEDist_add_edist
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {s : Set α},
Metric.infEDist x s ≤ Metric.infEDist y s + edist x yThe edist of x to s is bounded by the sum of the edist of y to s and
the edist from x to y
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- iInfproof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- add_commproof · cited by 1,535
- EDist.ediststatement and proof · cited by 735
- LE.le.trans_eqproof · cited by 328
- Metric.infEDiststatement · cited by 147
- PseudoEMetricSpace.edist_triangleproof · cited by 24
- iInf₂_monoproof · cited by 10
- ENNReal.iInf_addproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- Metric.infEDist_le_edist_add_infEDistproof · cited by 4
- Metric.infDist_le_infDist_add_distproof · cited by 2
- TopologicalSpace.Closeds.continuous_infEDistproof · cited by 1
- EMetric.infEdist_le_infEdist_add_edistproof · cited by 0