Theorems · Theorem · general topology
LipschitzWith.norm_sub_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddCommGroup E] [inst_1 : SeminormedAddCommGroup F] {f : E → F}
{C : NNReal}, LipschitzWith C f → ∀ (x y : E), ‖f x - f y‖ ≤ ↑C * ‖x - y‖Alias of the forward direction of lipschitzWith_iff_norm_sub_le.
- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- LipschitzWithstatement · cited by 316
- lipschitzWith_iff_norm_sub_leproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- LipschitzWith.comp_memLpproof · cited by 6
- LipschitzWith.hasFDerivAt_of_hasLineDerivAt_of_closureproof · cited by 1
- LipschitzWith.norm_sub_le_of_leproof · cited by 1
- LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mulproof · cited by 1
- LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'proof · cited by 1