Theorems · Theorem · functional analysis
NormedAddGroupHom.opNorm_le_of_lipschitz
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
{f : NormedAddGroupHom V₁ V₂} {K : NNReal}, LipschitzWith K ⇑f → ‖f‖ ≤ ↑K- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- 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
- map_zeroproof · cited by 1,614
- Dist.distproof · cited by 1,539
- NNReal.toRealstatement and proof · cited by 1,260
- LipschitzWithstatement and proof · cited by 316
- NormedAddGroupHomstatement and proof · cited by 216
- dist_zero_rightproof · cited by 172
- LipschitzWith.dist_le_mulproof · cited by 20
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