Theorems · Theorem · general topology
Metric.AreSeparated.union_left
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {s t s' : Set X},
Metric.AreSeparated s t → Metric.AreSeparated s' t → Metric.AreSeparated (s ∪ s') t- Cited by
- 2 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.
Cites10
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
- ENNRealproof · cited by 9,879
- LE.le.transproof · cited by 3,151
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
- pos_iff_ne_zeroproof · cited by 180
- min_le_leftproof · cited by 105
- min_le_rightproof · cited by 88
- lt_minproof · cited by 69
- Metric.AreSeparatedstatement and proof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Metric.AreSeparated.union_left_iffproof · cited by 2
- Metric.AreSeparated.union_rightproof · cited by 0