Theorems · Theorem · general topology
lipschitzOnWith_iff_norm_inv_mul_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedGroup E] [inst_1 : SeminormedGroup F] {s : Set E} {f : E → F}
{C : NNReal}, LipschitzOnWith C f s ↔ ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃y : E⦄, y ∈ s → ‖(f x)⁻¹ * f y‖ ≤ ↑C * ‖x⁻¹ * y‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 2 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.
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 and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- SeminormedGroupstatement and proof · cited by 250
- LipschitzOnWithstatement · cited by 164
- dist_eq_norm_inv_mulproof · cited by 41
Cited by2
Results whose statement or proof uses this declaration.
- lipschitzOnWith_iff_norm_div_leproof · cited by 1
- LipschitzOnWith.norm_inv_mul_leproof · cited by 1