Theorems · Theorem · general topology
LipschitzOnWith.norm_sub_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddCommGroup E] [inst_1 : SeminormedAddCommGroup F] {f : E → F}
{C : NNReal} {s : Set E}, LipschitzOnWith C f s → ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃y : E⦄, y ∈ s → ‖f x - f y‖ ≤ ↑C * ‖x - y‖Alias of the forward direction of lipschitzOnWith_iff_norm_sub_le.
- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 7 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.
Cites8
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 · cited by 25,697
- Norm.normstatement · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNReal.toRealstatement · cited by 1,260
- LipschitzOnWithstatement · cited by 164
- lipschitzOnWith_iff_norm_sub_leproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- hasFDerivAt_integral_of_dominated_loc_of_lipproof · cited by 4
- norm_fderiv_le_of_lipschitzOnproof · cited by 2
- HasFDerivAt.le_of_lipschitzOnproof · cited by 2
- HasLineDerivAt.le_of_lipschitzOnproof · cited by 1
- norm_lineDeriv_le_of_lipschitzOnproof · cited by 1
- IsPicardLindelof.of_contDiffAt_oneproof · cited by 1
- LipschitzOnWith.norm_sub_le_of_leproof · cited by 0