Theorems · Theorem · general topology
LipschitzWith.cauchySeq_comp
∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {f : α → β},
LipschitzWith K f → ∀ {u : ℕ → α}, CauchySeq u → CauchySeq (f ∘ u)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- nhdsproof · cited by 5,554
- NNRealstatement and proof · cited by 4,310
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- MulZeroClass.mul_zeroproof · cited by 2,091
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- NNReal.toRealproof · cited by 1,260
- mul_nonnegproof · cited by 397
- LipschitzWithstatement and proof · cited by 316
- CauchySeqstatement and proof · cited by 131
Cited by3
Results whose statement or proof uses this declaration.
- SeparatingDual.completeSpace_of_completeSpace_continuousLinearMapproof · cited by 1
- SeparatingDual.completeSpace_of_completeSpace_continuousMultilinearMapproof · cited by 1
- MeasureTheory.completeSpace_of_completeSpace_Lpproof · cited by 1