Theorems · Theorem · general topology
thickenedIndicatorAux_mono_infEDist
∀ {α : Type u_1} [inst : PseudoEMetricSpace α] (δ : ℝ) {E : Set α} {x y : α},
Metric.infEDist x E ≤ Metric.infEDist y E → thickenedIndicatorAux δ E y ≤ thickenedIndicatorAux δ E x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 149 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.
Cites13
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
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- LE.le.transproof · cited by 3,151
- le_reflproof · cited by 2,061
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofRealproof · cited by 863
- le_totalproof · cited by 294
- Metric.infEDiststatement and proof · cited by 147
- tsub_eq_zero_of_leproof · cited by 26
- thickenedIndicatorAuxstatement · cited by 21
- ENNReal.div_le_divproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- lipschitzWith_thickenedIndicatorproof · cited by 1
- thickenedIndicator_mono_infEDistproof · cited by 1
- thickenedIndicatorAux_mono_infEdistproof · cited by 0