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Theorems · Theorem · general topology

lipschitzWith_neg_iff

∀ {α : Type u_4} {E : Type u_5} [inst : SeminormedAddCommGroup E] [inst_1 : PseudoEMetricSpace α] {K : NNReal}
  {f : α → E}, LipschitzWith K (-f) ↔ LipschitzWith K f
Defined in
Mathlib.Analysis.Normed.Group.Uniform
Cited by
2 results in Mathlib
Foundations
Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupPseudoEMetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LipschitzWith.neg · cited by 3LipschitzWith.negLipschitzWith.of_neg · cited by 0LipschitzWith.of_negNNReal · cited by 4310NNRealSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealEDist.edist · cited by 735EDist.edistLipschitzWith · cited by 316LipschitzWithedist_neg_neg · cited by 6edist_neg_neglipschitzWith_neg_iffCITED BYCITES

Cites7

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Cited by2

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