Theorems · Theorem · general topology
LipschitzWith.id
∀ {α : Type u} [inst : PseudoEMetricSpace α], LipschitzWith 1 idThe identity is 1-Lipschitz.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 8 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- le_rflproof · cited by 1,558
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LipschitzWithstatement · cited by 316
- LipschitzWith.of_edist_leproof · cited by 12
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.lipschitzWith_pos_partproof · cited by 3
- ODE_solution_unique_of_mem_Icc_leftproof · cited by 2
- LipschitzWith.prodMk_leftproof · cited by 1
- LipschitzWith.prodMk_rightproof · cited by 1
- LipschitzWith.projIccproof · cited by 1
- lipschitzWith_negPartproof · cited by 1
- holderWith_idproof · cited by 0
- LocallyLipschitz.idproof · cited by 0