Theorems · Theorem · general topology
LipschitzOnWith.norm_inv_mul_le_of_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedGroup E] [inst_1 : SeminormedGroup F] {s : Set E} {a b : E} {r : ℝ}
{f : E → F} {C : NNReal}, LipschitzOnWith C f s → a ∈ s → b ∈ s → ‖a⁻¹ * b‖ ≤ r → ‖(f a)⁻¹ * f b‖ ≤ ↑C * r- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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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 and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- NNReal.toRealstatement · cited by 1,260
- mul_le_mul_of_nonneg_leftproof · cited by 361
- SeminormedGroupstatement and proof · cited by 250
- LipschitzOnWithstatement and proof · cited by 164
- NNReal.coe_nonnegproof · cited by 130
- LipschitzOnWith.norm_inv_mul_leproof · cited by 1
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